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

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

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 mo...

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Veröffentlicht in:The Ramanujan journal 2016-11, Vol.41 (1-3), p.233-267
Hauptverfasser: Franc, Cameron, Mason, Geoffrey
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Hypergeometric functions
Mathematics
Mathematics and Statistics
Number Theory
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Beschreibung
Zusammenfassung: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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-014-9644-x