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arXiv · 1812.11322

On a $q$-deformation of modular forms

Victor J. W. Guo·Wadim Zudilin
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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.

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Victor J. W. Guo, Wadim Zudilin. 2019-03-21. On a $q$-deformation of modular forms. https://doi.org/10.1016/j.jmaa.2019.03.035

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