On a q-deformation of modular forms

By Victor J. W. Guo, Wadim Zudilin. Journal of Mathematical Analysis and Applications, 2018

50 citations recorded by the source corpus.

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, 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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c1a035aa0dfeb9792943382f3d937b0e421256c6