The action of Hecke operators on hypergeometric functions. In: J. Aust. Math. Soc., vol. 89, no. 1, pp. 51–74, 2010, ISSN: 1446-7887.
Abstract
We study the action of the Hecke operators Un on the set of hypergeometric 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 eigenfunctions, we also obtain an apriori unrelated result regarding the behavior of completely multiplicative hypergeometric coefficients.
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@article{MRS.2010,
title = {The action of Hecke operators on hypergeometric functions},
author = {Victor H. Moll and Sinai Robins and Kirk Soodhalter},
url = {http://arxiv.org/abs/1005.2946},
doi = {10.1017/S1446788710001461},
issn = {1446-7887},
year = {2010},
date = {2010-01-01},
urldate = {2010-01-01},
journal = {J. Aust. Math. Soc.},
volume = {89},
number = {1},
pages = {51\textendash74},
abstract = {We study the action of the Hecke operators Un on the set of hypergeometric 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 eigenfunctions, we also obtain an apriori unrelated result regarding the behavior of completely multiplicative hypergeometric coefficients.},
keywords = {published},
pubstate = {published},
tppubtype = {article}
}