Congruences for Ramanujan's f and {\omega} functions via generalized Borcherds products

TL;DR

This paper explores congruences related to Ramanujan's mock theta functions f and ω by applying the theory of generalized Borcherds products, connecting Maass forms and modular form congruences.

Contribution

It provides a detailed example of how generalized Borcherds products can be used to derive congruences for Ramanujan's mock theta functions.

Findings

Derived new congruences for Ramanujan's f and ω functions.

Connected Maass form coefficients with classical modular form congruences.

Extended the application of Borcherds products to mock theta functions.

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.