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arxiv: 1503.05519 · v1 · pith:MJGGHO3Ynew · submitted 2015-03-18 · 🧮 math.NT

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

Cameron Franc , Geoffrey Mason This is my paper
classification 🧮 math.NT
keywords modularequationsformsconnectionsdifferentialhypergeometricseriestheory
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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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