Journal of the Ramanujan Mathematical Society

Stephanie Treneer ¹

Affiliations
1 Department of Mathematics, Western Washington University, Bellingham, Washington 98225, US

Abstract

Linear congruences have been shown to exist for the partition function and for several other arithmetic functions that are generated by weakly holomorphic modular forms. In previous work, the author showed that such congruences exist for the Fourier coefficients of any weakly holomorphic modular form in a large class. In this paper, quadratic twists are used to produce new congruences for the coefficients of these forms. To demonstrate our main theorems, we give new congruences for overpartitions, and extend a result of Penniston regarding congruences for ℓ-regular partitions.

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