English

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.

Keywords

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}
}
R2 v1 2026-06-22T08:56:25.055Z