List of Publications

 Submitted to journals and proceedings

  1. 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. Submitted, pp. 1-16. 2012. [url] [bib]


Refereed journal and proceeding publications


Computer algebra and theoretical aspects

  1. J. Bluemlein, S. Klein, C. Schneider, F. Stan A Symbolic Summation Approach to Feynman Integral Calculus. J. Symbolic Comput. 47, pp 1267-1289, 2012.  [pdf] [bib]

  2. M. Kauers, C. Schneider. A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations. In: Proc. of ISSAC 2011, Anton Leykin (ed.), pp. 201-208. 2011.  [pdf] [ps] [bib]

  3. 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]

  4. M. Kauers, C. Schneider.Partial Denominator Bounds for Partial Linear Difference Equations. In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 211-218.2010. [pdf] [ps] [bib]

  5. C. Schneider. Structural Theorems for Symbolic Summation. Appl. Algebra Engrg. Comm. Comput. 21(1), pp. 1-32. 2010. [pdf] [bib]

  6. C. Schneider. Parameterized Telescoping Proves Algebraic Independence of Sums. Ann. Comb. 14(4), pp. 533-552. 2010. [pdf] [bib]
  7. 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 (2010), pp 110-115. arXiv::1006.4797 [math-ph]. [url] [bib]
  8. 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. [pdf] [bib]

  9. C. Schneider. A Refined Difference Field Theory for Symbolic Summation. J. Symbolic Comput. 43(9), pp. 611-644. 2008. [pdf] [bib]

  10. C. Schneider. Simplifying Sums in PiSigma-Extensions. J. Algebra Appl. 6(3), pp. 415-441. 2007. [ps] [pdf] [bib]

  11. M. Kauers, C. Schneider. Symbolic Summation with Radical Expressions. In: Proc. ISSAC'07, C. W. Brown (ed.), pp. 219-226. 2007. ACM Press  [pdf] [ps] [bib]
  12.  M. Kauers, C. Schneider. Indefinite Summation with Unspecified Summands. Discrete Math., 306(17), pp. 2073-2083. 2006. Preliminary version online. [pdf] [bib]

  13. M. Kauers, C. Schneider. Application of Unspecified Sequences in Symbolic Summation. In: Proc. ISSAC'06, Jean-Guillaume Dumas (ed.),  pp. 177-183. 2006. ACM Press, [ps] [pdf] [bib]

  14.  C. Schneider. Product Representations in PiSigma-Fields. Annals of Combinatorics, 9(1), pp. 75-99. 2005. Preliminary version online. [pdf] [ps] [bib]

  15. 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. Preliminary version online. [ps] [pdf] [bib]

  16. C. Schneider. Degree Bounds To Find Polynomial Solutions of Parameterized Linear Difference Equations in PiSigma-Fields. Appl. Algebra Engrg. Comm. Comput., 16(1), pp. 1-32. 2005. Preliminary version online. [pdf] [ps] [bib]

  17. 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. Preliminary version online. [pdf] [ps] [bib]

  18. 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 Press. [pdf] [ps] [bib]

  19. C. Schneider. Symbolic Summation with Single-Nested Sum Extensions. In: Proc. ISSAC'04, J. Gutierrez (ed.), pp. 282-289. 2004. ACM Press. [pdf] [ps] [bib]

  20. A Collection of Denominator Bounds to Solve Parameterized Linear Difference Equations in PiSigma-Extensions. An. Univ. Timisoara Ser. Mat.-Inform., 42(2), pp. 163-179. 2004 .Extended version of Proc. SYNASC'04; preliminary version online. [pdf] [ps] [bib]

  21. C. Schneider. An Implementation of Karr's Summation Algorithm in Mathematica. Sem. Lothar. Combin. S43b, pp. 1-10. 2000. [url] [pdf] [ps] [bib]



Applications (e.g., special functions, number theory, particle physic)

  1. 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 (2012), pp. 52-84 [url] [bib]

  2. 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]

  3. J. Ablinger, J. Bluemlein, C. Schneider. Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. J. Math. Phys. 52(10), pp. 1-52. 2011.  [pdf] [bib]

  4. H. Prodinger, C. Schneider, S. Wagner. Unfair permutations. Europ. J. Comb. 32, pp. 1282-1298. 2011. [pdf] [bib]

  5. 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. [url] [bib]
  6. 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 (2010), pp 242-249. arXiv::1007.0375 [hep-ph]. [url] [bib]

  7. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. [pdf] [bib]

  8. 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. [url] [pdf] [bib]

  9. Manuel Kauers , Carsten Schneider. Automated Proofs for Some Stirling Number Identities. The Electronic Journal of Combinatorics 15(1), pp. 1-7. 2008. R2. [pdf] [ps] [bib]

  10. C. Schneider, R. Osburn. Gaussian Hypergeometric series and supercongruences. Math. Comp. 78(275-292), pp. 1-19. [url] [pdf] [bib]

  11. 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.  [url] [pdf] [bib]

  12. 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. [pdf] [bib]

  13. P. Paule, C. Schneider. Truncating Binomial Series with Symbolic Summation. INTEGERS. Electronic Journal of Combinatorial Number Theory(7), #A22., pp. 1-9. 2007.  [url] [pdf] [bib]

  14. C. Schneider, R. Pemantle. When is 0.999... equal to 1?. Amer. Math. Monthly, 114(4), pp. 344-350. 2007. Preliminary version online. [ps] [pdf] [bib]

  15. C. Schneider. Apery's Double Sum is Plain Sailing Indeed. Electron. J. Combin., 14, #N5, pp. 1-3. 2007. [url] [pdf] [ps] [bib]
  16. C. Schneider. Symbolic Summation Assists Combinatorics. Sem. Lothar. Combin., 56, Article B56b, pp. 1-36. 2007. [url] [pdf] [ps] [bib]

  17. 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. Preliminary version available. [pdf] [ps] [bib]

  18. 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. 2006. Preliminary version online. [url] [pdf] [ps] [bib]

  19. 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. Preliminary version online. [pdf] [ps] [ps] [bib]

  20. 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. Preliminary version online. [ps] [pdf] [bib]

  21. C. Schneider. The Summation Package Sigma: Underlying Principles and a Rhombus Tiling Application. Discrete Math. Theor. Comput. Sci., 6(2), pp. 365-386. 2004. [url][pdf] [ps] [bib]

  22. P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math., 31(2), pp. 359-378. 2003. Preliminary version online. [pdf][ps] [bib]




Other publications
  1. J. Ablinger, J. Bluemlein, S. Klein, C. Schneider, F. Wissbrock. 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines. To appear in Proc. of 19th International Workshop On Deep-Inelastic Scattering And Related Subjects (DIS 2011). [url] [bib]
  2. J. Bluemlein, S. Klein, C. Schneider, F. Stan. A symbolic summation approach to Feynman integrals. ACM SIGSAM Bulletin 44(3/4), pp. 95-96. 2010. ISSN:0163-5824 . [bib]

  3. 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. [bib]

  4. J. Bluemlein, M. Kauers, S. Klein, C. Schneider. From Moments to Functions in Quantum Chromodynamics. In Proc. ACAT 2008, PoS(ACAT08)106. [ps] [pdf] [bib]

  5. S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007, PoS(ACAT)083, pp. 1-11. 2007. [url] [pdf] [bib]

  6. I. Bierenbaum, J. Blümlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007,  PoS(ACAT)082, pp. 1-15. 2007. [url] [pdf] [bib]

  7. C. Schneider. Parameterized telescoping proves algebraic independence of sums. 2007. Poster presentation at FPSAC 2007. [url] [pdf] [pdf] [bib]

  8. 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. [url] [pdf] [bib]

  9. 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. [pdf] [ps] [bib]


Theses
  1. C. Schneider. Multi-Summation in Difference Fields RISC, J. Kepler University Linz, Habilitation. March 2007.

  2. C. Schneider. Symbolic Summation in Difference Fields. RISC, J. Kepler University Linz. PhD Thesis (advisor P. Paule). May 2001. (published as Technical report no. 01-17 in RISC Report Series). [pdf][ps] [bib]

  3. 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 (advisor V. Strehl). [pdf] [ps][bib]