Congruences for Ramanujan's f and {\omega} functions via generalized Borcherds products
Number Theory
2014-12-30 v1
Abstract
Bruinier and Ono recently developed the theory of generalized Borcherds products, which uses coefficients of certain Maass forms as exponents in infinite product expansions of meromorphic modular forms. Using this, one can use classical results on congruences of modular forms to obtain congruences for Maass forms. In this note we work out the example of Ramanujan's mock theta functions f and {\omega} in detail.
Keywords
Cite
@article{arxiv.1308.3454,
title = {Congruences for Ramanujan's f and {\omega} functions via generalized Borcherds products},
author = {Jen Berg and Abel Castillo and Robert Grizzard and Vítězslav Kala and Richard Moy and Chongli Wang},
journal= {arXiv preprint arXiv:1308.3454},
year = {2014}
}
Comments
10 pages, 1 table. To appear in The Ramanujan Journal