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

Cameron Franc; Geoffrey Mason

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arXiv · 1503.05519

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

Cameron Franc·Geoffrey Mason

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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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Cameron Franc, Geoffrey Mason. 2015-03-18. Hypergeometric series, modular linear differential equations, and vector-valued modular forms. https://arxiv.org/abs/1503.05519

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