@ARTICLE{MRS.2010,
  author = {Moll, Victor H. and Robins, Sinai and Soodhalter, Kirk},
  title = {The action of {H}ecke operators on hypergeometric functions},
  journal = {J. Aust. Math. Soc.},
  year = {2010},
  volume = {89},
  pages = {51--74},
  number = {1},
  abstract = {We study the action of the Hecke operators \(\lbrace U_{n} \rbrace_{1}^{\\infty}\)
	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 \(\lbrace na:n\\in \mathbb N
	, a\\in \mathbb Z \rbrace\), and that the polylogarithms play an
	important role in the study of the eigenfunctions of the Hecke operators
	\(\lbrace U_{n} \rbrace_{1}^{\\infty}\) on the set of hypergeometric
	functions. As a corollary of our results on simultaneous eigenfunctions,
	we also obtain an apparently unrelated result regarding the behavior
	of completely multiplicative hypergeometric coefficients.},
  doi = {10.1017/S1446788710001461},
  fjournal = {Journal of the Australian Mathematical Society},
  issn = {1446-7887},
  keywords = {paper},
  mrclass = {11F25 (33C05 33C70)},
  mrnumber = {2727063 (2011m:11086)},
  mrreviewer = {Thomas R. Shemanske},
  owner = {kirk},
  timestamp = {2012.08.16},
  url = {http://arxiv.org/abs/1005.2946}
}