RISC JKU
  • @article{RISC3969,
    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−π‘žπ›Ώπ‘›)π‘Ÿπ›Ώ=∑∞𝑛=0π‘Ž(𝑛)π‘žπ‘› and three positive integers m,t,p, and which returns true if π‘Ž(π‘šπ‘›+𝑑)≡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}
    }