V. P. Spiridonov, “Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type”, TMF, 2003, Volume 135, Number 3,Pages <nobr>462

This article is cited in 4 papers

Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type

V. P. Spiridonov^ab

^a Joint Institute for Nuclear Research
^b Max Planck Institute for Mathematics

Abstract: We collect some new evidence for the validity of the conjecture that every totally elliptic hypergeometric series is modular invariant and briefly discuss a generalization of such series to Riemann surfaces of arbitrary genus.

Keywords: theta functions, elliptic hypergeometric series, modular group, summation formulas.

DOI: 10.4213/tmf203