The action of Hecke operators on hypergeometric functions
Number Theory
2010-05-18 v1 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.1005.2946,
title = {The action of Hecke operators on hypergeometric functions},
author = {Victor H. Moll and Sinai Robins and Kirk Soodhalter},
journal= {arXiv preprint arXiv:1005.2946},
year = {2010}
}
Comments
23 pages