Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

Madeline Locus Dawsey, Dermot McCarthy

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely used in, character sum evaluations and counting points on algebraic varieties. More interestingly, perhaps, are their links to Fourier coefficients of modular forms. In this paper, we outline the main results in this area and also conjecture 13 new relations.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages41-56
Number of pages16
DOIs
StatePublished - 2021

Publication series

NameOperator Theory: Advances and Applications
Volume285
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Hypergeometric functions
  • Modular forms

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