On a $q$-deformation of modular forms

Abstract

There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite $q$-hypergeometric sums at roots of unity. Here we combine the two features to construct a hypergeometric $q$-deformation of two CM modular forms of weight 3 and discuss the corresponding $q$-congruences.

13 pages

References in corpus (1)

• Some new $q$-congruences for truncated basic hypergeometric series

Cited by in corpus (9)

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• A family of $q$-congruences modulo the square of a cyclotomic polynomial
• Some $q$-supercongruences modulo the fourth power of a cyclotomic polynomial
• A further $q$-analogue of Van Hamme's (H.2) supercongruence for $p\equiv 1(\mathrm{mod}4)$
• The united proofs for three $q$-extensions of Dougall's ${}_2{H}_2$ summation formula