author = {Silviu Radu},
title = {{An algorithmic approach to Ramanujan congruences }},
language = {english},
abstract = {In this paper we present an algorithm that takes as input a generating function of the form ∏𝛿|𝑀∏∞𝑛=1(1−𝑞𝛿𝑛)𝑟𝛿=∑∞𝑛=0𝑎(𝑛)𝑞𝑛 and three positive integers m,t,p, and which returns true if 𝑎(𝑚𝑛+𝑡)≡0(mod𝑝),𝑛≥0, or false otherwise. Our method builds on work by Rademacher (Trans. Am. Math. Soc. 51(3):609–636, 1942), Kolberg (Math. Scand. 5:77–92, 1957), Sturm (Lecture Notes in Mathematics, pp. 275–280, Springer, Berlin/Heidelberg, 1987), Eichhorn and Ono (Proceedings for a Conference in Honor of Heini Halberstam, pp. 309–321, 1996).},
journal = {Ramanujan Journal},
volume = {20},
number = {2},
pages = {215--251},
isbn_issn = {1382-4090 },
year = {2009},
refereed = {yes},
length = {37},
url = {https://doi.org/10.1007/s11139-009-9174-0}