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

By C. Franc, Geoffrey Mason. 2015

66 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/56622b2f50dd0b76140475e28dc3eeb4fb9d2b5e