Hypergeometric series, modular linear differential equations, and vector-valued modular forms

2015/03/18 by Franc, Cameron, Mason, Geoffrey · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1503.05519

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.

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