Hypergeometric series, modular linear differential equations, and vector-valued modular forms
Number Theory
2015-03-19 v1
Abstract
We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the three-punctured sphere. We present a number of numerical examples showing how the theory in dimensions 2 and 3 leads naturally to close connections between modular forms and hypergeometric series.
Cite
@article{arxiv.1503.05519,
title = {Hypergeometric series, modular linear differential equations, and vector-valued modular forms},
author = {Cameron Franc and Geoffrey Mason},
journal= {arXiv preprint arXiv:1503.05519},
year = {2015}
}