The action of Hecke operators on hypergeometric functions

Details The action of Hecke operators on hypergeometric functions The action of Hecke operators on hypergeometric functions

2010-05-17

arxiv.org/abs/1005.2946v1

Mathematics

Number Theory

23 pages

Scientific paper

We study the action of the Hecke operators Un on the set of hy- pergeometric functions, as well as on formal power series. We show that the spectrum of these operators on the set of hypergeometric functions is the set n^a with a an integer and n a positive integer, and that the polylogarithms play a dominant role in the study of the eigenfunctions of the Hecke operators Un on the set of hypergeometric functions. As a corollary of our results on simultaneous eigen- functions, we also obtain an apriori unrelated result regarding the behavior of completely multiplicative hypergeometric coefficients.

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