A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform

Dermot McCarthy, Matthew A. Papanikolas

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Although links between values of finite field hypergeometric functions and eigenvalues of elliptic modular forms are well known, we establish in this paper that there are also connections to eigenvalues of Siegel modular forms of higher degree. Specifically, we relate the eigenvalue of the Hecke operator of index p of a Siegel eigenform of degree 2 and level 8 to a special value of a 4F3-hypergeometric function.

Original languageEnglish
Pages (from-to)2431-2450
Number of pages20
JournalInternational Journal of Number Theory
Volume11
Issue number8
DOIs
StatePublished - Dec 1 2015

Keywords

  • Gauss sums
  • Hecke eigenvalues
  • Hypergeometric functions
  • Siegel modular forms
  • finite fields

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