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Hypergeometric series, modular linear differential equations, and vector-valued modular forms (1503.05519v1)
Published 18 Mar 2015 in math.NT
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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