On a $q$-deformation of modular forms
Number Theory
2019-04-04 v2 Algebraic Geometry
Classical Analysis and ODEs
Combinatorics
Quantum Algebra
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 -hypergeometric sums at roots of unity. Here we combine the two features to construct a hypergeometric -deformation of two CM modular forms of weight 3 and discuss the corresponding -congruences.
Cite
@article{arxiv.1812.11322,
title = {On a $q$-deformation of modular forms},
author = {Victor J. W. Guo and Wadim Zudilin},
journal= {arXiv preprint arXiv:1812.11322},
year = {2019}
}
Comments
13 pages