Geodesic
Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 462-477

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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. 
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     author = {V. P. Spiridonov},
     title = {Modularity and {Total} {Ellipticity} of {Some} {Multiple} {Series} of {Hypergeometric} {Type}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {462--477},
     publisher = {mathdoc},
     volume = {135},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a8/}
}
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V. P. Spiridonov. Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 462-477. http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a8/