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Carsten Schneider, Assoc. Prof. DI Dr.

RISC Faculty

Publications

C. Schneider. Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects. J. Symb. Comput. 80(3), pp. 616-664. 2017. ISSN 0747-7171. arXiv:1603.04285 [cs.SC]. [url] [bib]
C. Schneider, R. Sulzgruber. Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm. Electron. J. Combin. 24(2), pp. 1-33. 2017. ISSN: 1077-8926. #P2.28, arXiv:1606.07597. [url] [bib]
J. Blümlein, C. Schneider. The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory. Physics Letters B 771, pp. 31-36. 2017. ISSN 0370-2693. arXiv:1701.04614 [hep-ph]. [url] [bib]
J. Middeke, C. Schneider. Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions. In: Advances in Computer Algebra, C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics , pp. 1-24. 2017. arXiv:1705.00280 [cs.SC]. [url] [bib]
E.D. Ocansey, C. Schneider. Representing (q-)hypergeometric products and mixed versions in difference rings. In: Advances in Computer Algebra,, C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics , pp. 1-36. 2017. arXiv:1705.01368 [cs.SC]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider. The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, \rm N_F)}$. Nucl. Phys. B. 922, pp. 1-40. 2017. ISSN 0550-3213.. arXiv:1705.01508 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, C. Schneider, F. Wißbrock. Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses. Nucl. Phys. B. 921, pp. 585-688. 2017. ISSN 0550-3213. arXiv:1705.07030 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C.G. Raab, C.-S. Radu, C. Schneider. Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams. submitted, pp. 1-68. 2017. arXiv:1706.01299 [hep-th]. [url] [bib]
J. Blümlein, M. Round, C. Schneider. Refined Holonomic Summation Algorithms in Particle Physics. In: Advances in Computer Algebra, E. Zima, C. Schneider (ed.), Springer Proceedings in Mathematics & Statistics , pp. 1-39. 2017. Springer, arXiv:1706.03677 [cs.SC]. [url] [bib]
J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald. The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization. Cornell University. Technical report no. arXiv:1710.04500 [hep-ph], 2017. [bib]
C. Schneider. A Difference Ring Theory for Symbolic Summation. J. Symb. Comput. 72, pp. 82-127. 2016. ISSN 0747-7171. arXiv:1408.2776 [cs.SC]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider. Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra. Comput. Phys. Comm. 202, pp. 33-112. 2016. ISSN 0010-4655. arXiv:1509.08324 [hep-ph]. [url] [bib]
J. Middeke, C. Schneider. Denominator Bounds for Higher Order Systems of Linear Recurrence Equations. ACM Communications in Computer Algebra 50(4), pp. 185-187. 2016. ISSN 1932-2240. Extended abstract of the poster presentation at ISSAC 2016. [pdf] [bib]
C. Schneider. Symbolic Summation in Difference Rings and Applications. In: Proc. ISSAC 2016, M. Rosenkranz (ed.), pp. 9-12. 2016. ISBN 978-1-4503-4380-0/16/07. [pdf] [bib]
E.D. Ocansey, C. Schneider. Representation of hypergeometric products in difference rings. ACM Communications in Computer Algebra 50(4), pp. 161-163. 2016. ISSN 1932-2240 . Extended abstract of the poster presentation at ISSAC 2016. [pdf] [bib]
C. Krattenthaler, C. Schneider. Evaluation of binomial double sums involving absolute values. submitted, pp. 1-36. 2016. arXiv:1607.05314 [math.CO]. [url] [bib]
J. Ablinger, A. Behring, J. Bluemlein, A. de Freitas, C. Schneider. Algorithms to solve coupled systems of differential equations in terms of power series. In: Proc. Loops and Legs in Quantum Field Theory - LL 2016, J. Bluemlein, P. Marquard, T. Riemann (ed.) (ed.)PoS(LL2016)005, pp. 1-15. 2016. ISSN 1824-8039. arXiv:1608.05376 [cs.SC]. [url] [bib]
A. Behring, J. Blümlein, G. Falcioni, A. De Freitas, A. von Manteuffel, C. Schneider. The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^+-W^-}(x, Q^2)$ and $F_2^{W^+-W^-}(x, Q^2)$. Physical Review D 94(11), pp. 1-19. 2016. ISSN 1550-2368. arXiv:1609.06255 [hep-ph]. [url] [bib]
Jakob Ablinger, Arnd Behring, Johannes Blümlein, Abilio De Freitas, Alexander Hasselhuhn, Andreas von Manteuffel, Mark Round, Carsten Schneider, Fabian Wißbrock. Heavy flavour corrections to polarised and unpolarised deep-inelastic scattering at 3-loop order. In: Proceedings of the QCD Evolution 2016, PoS(QCDEV2016)052, pp. 1-16. 2016. National Institute for Subatomic Physics (Nikhef) in Amsterdam, ISSN 1824-8039. arXiv:1611.01104 [hep-ph]. [url] [bib]
J. Ablinger, J. Behring, J. Blümlein, G. Falcioni, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock. New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering. In: Proc. Loops and Legs in Quantum Field Theory - LL 2016, J. Bluemlein and P. Marquard and T. Riemann (ed.), Proc. of Sciences PoS (LL2016) 065, pp. 1-16. 2016. ISSN 1824-8039. arXiv:1609.03397 [hep-ph]. [url] [bib]
C. Schneider. Fast Algorithms for Refined Parameterized Telescoping in Difference Fields. In: Computer Algebra and Polynomials, Applications of Algebra and Number Theory, Jaime Gutierrez, Josef Schicho, Martin Weimann (ed.), Lecture Notes in Computer Science (LNCS) 8942, pp. 157-191. 2015. Springer, ISSN: 0302-9743 . arXiv:1307.7887 [cs.SC]. [url] [bib]
J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider. 3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$. In: 17th International Conference in Quantum Chromodynamics (QCD 14), Stephan Narison (ed.), Proceedings of QCD Montpellier Conference, Nucl. Phys. B (Proc. Suppl.) 258-259, pp. 37-40. 2015. ISSN 0550-3213. arXiv:1409.1435 [hep-ph]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider. The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x, Q^2)$ and the Anomalous Dimension. Nuclear Physics B 890, pp. 48-151. 2015. ISSN 0550-3213. arXiv:1409.1135 [hep-ph]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, S. Schneider, F. Wißbrock. 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering. In: 17th International Conference in Quantum Chromodynamics (QCD 14), Stephan Narison (ed.), Nucl. Phys. B (Proc. Suppl.) 258-259, pp. 41-44. 2015. ISSN 0550-3213. arXiv:1409.1804 [hep-ph]. [url] [bib]
J. Blümlein, A. De Freitas, C. Schneider. Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering. In: Advances in Computational Particle Physics, J. Blümlein, K. Jansen, M. Krämer, J.H. Kühn (ed.), Proceedings of Final Meeting of DFG SFB-TR-9, Nucl. Phys. B (Proc. Suppl.) , pp. 185-201. 2015. ISSN 0550-3213. arXiv:1411.5669 [hep-ph]. [url] [bib]
A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider. The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x, Q^2) at Large Momentum Transfer. Nucl. Phys. B 897, pp. 612-644. 2015. ISSN 0550-3213.. arXiv:1504.08217 [hep-ph]. [url] [bib]
A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Schneider. The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x, Q^2) at Large Momentum Transfer. Physical Review D 92(114005), pp. 1-19. 2015. ISSN 1550-2368. arXiv:1508.01449 [hep-ph]. [url] [bib]
J. Ablinger, C. Schneider. Algebraic independence of (cyclotomic) harmonic sums. In: submitted, , pp. -. 2015. arXiv:1510.03692 [cs.SC]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C.G. Raab, M. Round, C. Schneider, F. Wißbrock. 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. In: Proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP), PoS(EPS-HEP2015)504, pp. 1-13. 2015. ISSN 1824-8039. arXiv:1602.00583 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, A. de Freitas, C. Schneider. A toolbox to solve coupled systems of differential and difference equations. In: Proc. of 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders), - (ed.)PoS(RADCOR2015)060, pp. 1-13. 2015. ISSN 1824-8039.. arXiv:1601.01856 [cs.SC]. [url] [bib]
C. Schneider. Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction. In: Proc. ACAT 2013, , J. Phys.: Conf. Ser. 523/012037, pp. 1-17. 2014. ISSN 1742-6596. arXiv:1310.0160 [cs.SC]. [url] [bib]
J. Ablinger, J. Bluemlein, C. Schneider. Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers. In: Proc. ACAT 2013, , J. Phys.: Conf. Ser 523/012060, pp. 1-10. 2014. ISSN 1742-6596. arXiv:1310.5645 [math-ph]. [url] [bib]
J. Ablinger, J. Bluemlein, A. De Freitas A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock. The Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O(\alpha_s^3)$. Nuclear Physics B 882, pp. 263-288. 2014. ISSN: 0550-3213. arXiv:1402.0359 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, C. Raab, C. Schneider, F. Wissbrock. Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms. Nuclear Physics B 885, pp. 409-447. 2014. ISSN: 0550-3213. arXiv:1403.1137 [hep-ph]. [url] [bib]
J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider. The $O(\alpha_s^3 T_F^2)$ Contributions to the Gluonic Operator Matrix Element. Nuclear Physics B 885, pp. 280-317. 2014. ISSN: 0550-3213. arXiv:1405.4259 [hep-ph]. [url] [bib]
J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock. The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for thE Structure Function \boldmath $F_2(x, Q^2)$ and Transversity. Nuclear Physics B 886, pp. 733-823. 2014. ISSN: 0550-3213. arXiv:1406.4654 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, C.G. Raab, C. Schneider. Iterated Binomial Sums and their Associated Iterated Integrals. J. Math. Phys. 55(112301), pp. 1-57. 2014. ISSN 0022-2488. arXiv:1407.1822 [hep-th]. [url] [bib]
A. De Freitas, J. Blümlein, C. Schneider. Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)017 , pp. 1-13. 2014. ISSN 1824-8039. arXiv:1407.2537 [cs.SC]. [url] [bib]
J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wißbrock. 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines. In: Proceedings of Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)015 , pp. 1-10. 2014. ISSN 1824-8039. arXiv:1407.2821 [hep-ph]. [url] [bib]
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wißbrock. Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)041 , pp. 1-11. 2014. ISSN 1824-8039. arXiv:1407.3638 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, C G. Raab, C. Schneider. Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)020 , pp. 1-13. 2014. ISSN 1824-8039. arXiv:1407.4721 [hep-th]. [url] [bib]
J. Blümlein, I. Dubovyk, J. Gluza, M. Ochman, C.G. Raab, T. Riemann, C. Schneider. Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums. In: Loops and Legs in Quantum Field Theory - LL 2014, J. Bluemlein, P. Marquard, T. Riemann (ed.), PoS(LL2014)52 , pp. 1-14. 2014. ISSN 1824-8039. arXiv:1407.7832 [hep-ph]. [url] [bib]
C. Schneider. A streamlined difference ring theory: Indefinite nested sums, the alternating sign and the parameterized telescoping problem. In: Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 15th International Symposium, Franz Winkler, Viorel Negru, Tetsuo Ida, Tudor Jebelean, Dana Petcu, Stephen Watt, Daniela Zaharie (ed.), pp. 26-33. 2014. IEEE Computer Society, ISBN-13:978-1-4799-8448-0. arXiv:1412.2782v1 [cs.SC]. [url] [bib]
J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider. The $O(α_s^3 n_f T_F^2 C_{A, F})$} Contributions to the Gluonic Massive Operator Matrix Elements. Nuclear Physics B(866), pp. 196-211. 2013. ISSN: 0550-3213. [url] [pdf] [bib]
J. Ablinger, J. Bluemlein, C. Schneider. Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms. J. Math. Phys. 54, 082301 (2013); 54(082301), pp. 1-74. 2013. ISSN 0022-2488. arXiv:1302.0378 [math-ph]. [url] [pdf] [bib]
C. Schneider. Simplifying Multiple Sums in Difference Fields. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 325-360. 2013. Springer, ISBN-13: 978-3709116159. [url] [bib]
J. Bluemlein, T. Riemann, C. Schneider. Precision Calculations, Algebraic Summation and Integration - Towards the Mathematical Structure of the Microcosm. In: Annual report 2012 of the particle and astroparticle physics division at DESY, - (ed.), pp. 90-91. 2013. Deutsches Elektronen Synchrotron (DESY), -. [url] [bib]
S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann. Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC]. [url] [bib]
J. Bluemlein, C. Schneider (ed.). Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions. Texts and Monographs in Symbolic Computation, 2013. Springer Wien, ISBN-13: 978-3709116159. [bib]
J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Raab, M. Round, C. Schneider, F. Wissbrock. Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. In: XXI International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2013, PoS(DIS 2013)301, pp. 1-8. 2013. ISSN 1824-8039. arXiv:1307.7548 [hep-ph]. [url] [bib]
C. Schneider. Symbolic Summation in Difference Fields and Its Application in Particle Physics. Computer Algebra Rundbrief 53, pp. 8-12. 2013. ISSN 0933-5994. [url] [bib]
A. Behring, J. Bluemlein, A. De Freitas, T. Pfoh, C. Raab, M. Round, J. Ablinger, A. Hasselhuhn, C. Schneider, F. Wissbrock, A. von Manteuffel. New Results on the 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering. In: Proc. of RADCOR, , PoS(RADCOR 2013)058 , pp. 1-21. 2013. ISSN 1824-8039. arXiv:1312.0124 [hep-ph]. [url] [bib]
J. Bluemlein, S. Klein, C. Schneider, F. Stan. A Symbolic Summation Approach to Feynman Integral Calculus. J. Symbolic Comput. 47, pp. 1267-1289. 2012. ISSN 0747-7171. [pdf] [bib]
J. Ablinger, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock. New Heavy Flavor Contributions to the DIS Structure Function $F_2(x, Q^2)$ at $O(\alpha_s^3)$. In: Proceedings of RADCOR 2011, , Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) PoS(RADCOR2011)31, pp. 1-8. 2012. ISSN 1824-8039. [url] [bib]
J. Bluemlein, A. Hasselhuhn, C. Schneider. Evaluation of Multi-Sums for Large Scale Problems. In: Proceedings of RADCOR 2011, , Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)PoS(RADCOR2011)32, pp. 1-9. 2012. ISSN 1824-8039. [url] [bib]
J. Ablinger, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock. Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements. Nuclear Physics B 864, pp. 52-84. 2012. ISSN: 0550-3213. arXiv:1206.2252v1 [hep-ph]. [url] [bib]
J. Ablinger, J. Bluemlein, M. Round, C. Schneider. Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals. In: Loops and Legs in Quantum Field Theory 2012, J. Bluemlein, S. Moch, T. Riemann (ed.), PoS(LL2012) 50, pp. 1-14. 2012. ISSN 1824-8039. arXiv:1210.1685 [cs.SC]. [url] [bib]
J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, S. Klein, C. Raab, M. Round, C. Schneider, F. Wissbrock. Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N. In: Proc. Loops and Legs in Quantum Field Theory 2012, J. Blümlein, S. Moch, T. Riemann (ed.), PoS(LL2012)033 , pp. 1-12. 2012. ISSN 1824-8039. [url] [bib]
J. Ablinger, J. Bluemlein, A. De Freitas, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock. New Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering. In: Proceedings of the 36th International Conference on High Energy Physics, PoS(ICHEP2012)270, pp. 1-9. 2012. ISSN 1824-8039. [url] [bib]
J. Ablinger, J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. The O(\alpha_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x, Q^2) and Transversity. Nucl. Phys. B 844, pp. 26-54. 2011. .ISSN: 0550-3213. [url] [bib]
Manuel Kauers, Carsten Schneider. A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations. In: Proceedings of ISSAC 2011, Anton Leykin (ed.), pp. 201-208. 2011. 978-1-4503-0675-1. [pdf] [ps] [bib]
H. Prodinger, C. Schneider, S. Wagner. Unfair permutations. Europ. J. Comb. 32, pp. 1282-1298. 2011. ISSN: 0195-6698. [pdf] [bib]
J. Ablinger, J. Bluemlein, C. Schneider. Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. J. Math. Phys. 52(10), pp. 1-52. 2011. ISSN 0022-2488 . [arXiv:1007.0375 [hep-ph]]. [url] [pdf] [bib]
J. Ablinger, J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines. In: 19th International Workshop On Deep-Inelastic Scattering And Related Subjects (DIS 2011), , pp. -. 2011. American Institute of Physics (AIP), [url] [bib]
C. Schneider. Parameterized Telescoping Proves Algebraic Independence of Sums. Ann. Comb. 14(4), pp. 533-552. 2010. ISSN 0218-0006. arXiv:0808.2596. [pdf] [bib]
C. Schneider. A Symbolic Summation Approach to Find Optimal Nested Sum Representations. In: Motives, Quantum Field Theory, and Pseudodifferential Operators, A. Carey, D. Ellwood, S. Paycha, S. Rosenberg (ed.), Clay Mathematics Proceedings 12, pp. 285-308. 2010. Amer. Math. Soc, ISBN-10: 0-8218-5199-3. arXiv:0904.2323 . [pdf] [bib]
C. Schneider. Structural Theorems for Symbolic Summation. Appl. Algebra Engrg. Comm. Comput. 21(1), pp. 1-32. 2010. ISSN 0938-1279. [pdf] [bib]
Manuel Kauers, Carsten Schneider. Partial Denominator Bounds for Partial Linear Difference Equations. In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 211-218. 2010. 978-1-4503-0150-3. [pdf] [ps] [bib]
J. Ablinger, J. Bluemlein, S. Klein, C. Schneider. Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams . Nucl. Phys. B (Proc. Suppl.) 205-206, pp. 110-115. 2010. ISSN 0550-3213. arXiv::1006.4797 [math-ph], DESY-10-090, SFB-CPP-10-53, TTK-10-37. [url] [bib]
J. Ablinger, I. Bierenbaum, J. Bluemlein, A. Hasselhuhn, S. Klein, C. Schneider, F. Wissbrock. Heavy Flavor DIS Wilson coefficients in the asymptotic regime . Nucl. Phys. B (Proc. Suppl.) 205-206, pp. 242-249. 2010. ISSN 0550-3213. arXiv::1007.0375 [hep-ph], DESY-10-093, SFB-CPP-10-58, TTK-10-38. [url] [bib]
C. Schneider, R. Osburn. Gaussian Hypergeometric series and supercongruences. Math. Comp. 78(267), pp. 275-292. 2009. ISSN 0025-5718. [url] [pdf] [bib]
Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler. Algorithms in Symbolic Computation. In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [pdf] [bib]
J. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and {W}ilson coefficients from {M}ellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. ISSN 0010-4655. [pdf] [bib]
S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann. Computing the complexity for schelling segregation models. Communications in Nonlinear Science and Numerical Simulations 13, pp. 2236-2245. 2008. ISSN 1007-5704. [pdf] [bib]
C. Schneider. A Refined Difference Field Theory for Symbolic Summation. J. Symbolic Comput. 43(9), pp. 611-644. 2008. ISSN 0747-7171. arXiv:0808.2543 [cs.SC]. [pdf] [bib]
Manuel Kauers , Carsten Schneider. Automated Proofs for Some Stirling Number Identities. The Electronic Journal of Combinatorics 15(1), pp. 1-7. 2008. ISSN 1077-8926. R2. [pdf] [ps] [bib]
M. Kuba, H. Prodinger, C. Schneider. Generalized Reciprocity Laws for Sums of Harmonic Numbers. INTEGERS. Electronic Journal of Combinatorial Number Theory 8(A17), pp. 1-20. 2008. ISSN 1553-1732. [url] [pdf] [bib]
I. Bierenbaum, J. Bluemlein, S. Klein, C. Schneider. Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O!(epsilon)$. Nucl.Phys. B 803(1-2), pp. 1-41. November 2008. ISSN: 0550-3213. [url] [pdf] [bib]
J. Bluemlein, M. Kauers, S. Klein, C. Schneider. From moments to functions in higher order QCD . In: Proc. of Science, - (ed.), Proceedings of XII Advanced Computing and Analysis Techniques in Physics Research PoS(ACAT08)106, pp. 1-7. 2008. ISSN 1824-8039. [pdf] [bib]
C. Schneider, R. Pemantle. When is 0.999... equal to 1?. Amer. Math. Monthly 114(4), pp. 344-350. 2007. ISSN 0002-9890. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Simplifying Sums in ${\Pi}{\Sigma}^*$-Extensions. J. Algebra Appl. 6(3), pp. 415-441. 2007. ISSN: 0219-4988. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Symbolic Summation Assists Combinatorics. Sem. Lothar. Combin. 56, pp. 1-36. 2007. ISSN 1286-4889. Article B56b. [url] [ps] [pdf] [bib]
C. Schneider. {A}p\'{e}ry's Double Sum is Plain Sailing Indeed. Electron. J. Combin. 14(N5), pp. 1-3. 2007. ISSN 1077-8926. [url] [ps] [pdf] [bib]
M. Kauers, C. Schneider. Symbolic Summation with Radical Expressions. In: Proceedings of ISSAC'07, Christopher W. Brown (ed.), pp. 219-226. 2007. isbn 978-1-59593-743-8. [pdf] [ps] [bib]
P. Paule, C. Schneider. Truncating Binomial Series with Symbolic Summation. INTEGERS. Electronic Journal of Combinatorial Number Theory 7(A22), pp. 1-9. 2007. ISSN 1553-1732. [url] [pdf] [bib]
C. Schneider. Parameterized telescoping proves algebraic independence of sums. 2007. Poster presentation at FPSAC 2007. [url] [pdf] [pdf] [bib]
I. Bierenbaum, J. Blümlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)082, pp. 1-15. 2007. ISSN 18248039. [url] [pdf] [bib]
S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)083, pp. 1-11. 2007. ISSN 18248039. [url] [pdf] [bib]
C. Schneider. Multi-Summation in Difference Fields. 2007. Habilitation, [bib]
K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e Approximations to the logarithm II: Identities, recurrences, and symbolic computation. Ramanujan Journal 11(2), pp. 139-158. April 2006. ISSN 1382-4090. Preliminary version online. [url] [pdf] [ps] [bib]
K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e approximations to the logarithm III: Alternative methods and additional results. Ramanujan Journal 12(3), pp. 299-314. 2006. ISSN 1382-4090. Preliminary version online. [ps] [pdf] [ps] [bib]
C. Schneider. Some notes on ``When is 0.999... equal to 1?''. In: Mathematics, Algorithms, Proofs, T. Coquand et al. (ed.), Dagstuhl Seminar Proceedings 05021, pp. 1-3. 2006. Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, ISSN 1862-4405. [url] [pdf] [bib]
M. Kauers, C. Schneider. Indefinite summation with unspecified summands. Discrete Math. 306(17), pp. 2073-2083. 2006. ISSN 0012-365X. Preliminary version online. [pdf] [bib]
M. Kauers, C. Schneider. Application of unspecified sequences in symbolic summation. In: Proceedings of ISSAC'06, Jean-Guillaume Dumas (ed.), Proceedings of ISSAC'06, pp. 177-183. 2006. ACM Press, [pdf] [ps] [bib]
A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, J. Schoeberl. Hypergeometric Summation Algorithms for High Order Finite Elements. Computing 78(3), pp. 235-249. 2006. ISSN 0010-485X. Preliminary version available. [pdf] [ps] [bib]
P. Paule, V. Pillwein, C. Schneider, J. Schöberl. Hypergeometric Summation Techniques for High Order Finite Elements. In: PAMM, , Proceedings of GAMM Annual Meeting 2006 - Berlin6/1, pp. 689-690. 2006. Wiley InterScience, Weinheim, ISBN. DOI: 10.1002/pamm.200610325. [bib]
C. Schneider. Product Representations in $\Pi\Sigma$-Fields. Annals of Combinatorics 9(1), pp. 75-99. 2005. ISSN 0218-0006. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. A new Sigma approach to multi-summation. Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud 34(4), pp. 740-767. 2005. ISSN 0196-8858. Preliminary version online. [pdf] [ps] [bib]
G. E. Andrews, P. Paule, C. Schneider. Plane Partitions VI: Stembridge's TSPP Theorem. Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud 34(4), pp. 709-739. 2005. ISSN 0196-8858. Preliminary version online. [pdf] [ps] [bib]
C. Schneider. Degree Bounds To Find Polynomial Solutions of Parameterized Linear Difference Equations in $\Pi\Sigma$-Fields. Appl. Algebra Engrg. Comm. Comput. 16(1), pp. 1-32. 2005. ISSN 0938-1279. Preliminary version online. [pdf] [ps] [bib]
C. Schneider. Solving Parameterized Linear Difference Equations in Terms of Indefinite Nested Sums and Products. J. Differ. Equations Appl. 11(9), pp. 799-821. 2005. ISSN 1023-6198. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Finding Telescopers with Minimal Depth for Indefinite Nested Sum and Product Expressions (Extended Version). J. Kepler University Linz. Technical report no. 2005-08, 2005. SFB-Report. [ps] [pdf] [bib]
C. Schneider. Finding Telescopers with Minimal Depth for Indefinite Nested Sum and Product Expressions. In: Proc. ISSAC'05, M. Kauers (ed.), pp. 285-292. 2005. ACM, ISBN 1-59593-095-705/0007. [pdf] [ps] [bib]
C. Schneider. Symbolic Summation with Single-Nested Sum Extensions (Extended Version). J. Kepler University, Linz. Technical report no. 2004-7, 2004. Published in Proc. ISSAC'04. SFB-Report. [pdf] [ps] [bib]
C. Schneider. Symbolic Summation with Single-Nested Sum Extensions. In: Proc. ISSAC'04, J. Gutierrez (ed.), pp. 282-289. 2004. ACM Press, ISBN 1-58113-827-X. [pdf] [ps] [bib]
C. Schneider. The summation package Sigma: Underlying principles and a rhombus tiling application. Discrete Math. Theor. Comput. Sci. 6(2), pp. 365-386. 2004. ISSN 1365-8050. [url] [pdf] [ps] [bib]
G.E. Andrews, P. Paule, C. Schneider. Plane Partition VI: Stembridge's TSPP Theorem -- A detailed algorithmic proof. Technical report no. 04-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. May 2004. [ps] [pdf] [bib]
C. Schneider. A Collection of Denominator Bounds to Solve Parameterized Linear Difference Equations in ${\Pi}{\Sigma}$-Extensions. An. Univ. Timisoara Ser. Mat.-Inform. 42(2), pp. 163-179. 2004. ISSN 1224-970x. Extended version of Proc. SYNASC'04; preliminary version online. [pdf] [ps] [bib]
P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math. 31(2), pp. 359-378. 2003. ISSN 0196-8858. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. A Unique Representation of Solutions of Parameterized Linear Difference Equations in ${\Pi}{\Sigma}$-Fields. Technical report no. 02-06 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. July 2002. [ps] [bib]
C. Schneider. How one can play with sums. In: Proceedings of the 8th Rhine Workshop on Computer Algebra, H. Kredel, W. Seiler (ed.), pp. 73-83. 2002. Mannheim, Germany, -. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Symbolic Summation in Difference Fields. RISC, J. Kepler University Linz. PhD Thesis. May 2001. (published as Technical report no. 01-17 in RISC Report Series.). [ps] [pdf] [bib]
C. Schneider. An Implementation of {K}arr's Summation Algorithm in Mathematica. Sem. Lothar. Combin. S43b, pp. 1-10. 2000. ISSN 1286-4889. [url] [pdf] [ps] [bib]
C. Schneider. Implementierung von Automaten-Algorithmen mit Hilfe von binären Entscheidungsdiagrammen. Lehrstuhl für Künstliche Intelligenz (Informatik VIII), Friedrich Alexander Universität Erlangen-Nürnberg. Diploma Thesis. 1997. (Engl. translation: Implementation of Algorithms for Automatons with Binary Decision Diagrams - BDD). Diploma Thesis. [ps] [pdf] [bib]


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