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

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.

authors

• Papanikolas, Matthew

published proceedings

• INTERNATIONAL JOURNAL OF NUMBER THEORY

author list (cited authors)

• McCarthy, D., & Papanikolas, M. A.

citation count

• 15

complete list of authors

• McCarthy, Dermot||Papanikolas, Matthew A

publication date

• December 2015

publisher

• World Scientific Publishing  Publisher

published in

• International Journal of Number Theory  Journal

keywords

• Finite Fields
• Gauss Sums
• Hecke Eigenvalues
• Hypergeometric Functions
• Siegel Modular Forms

Digital Object Identifier (DOI)

• 10.1142/S1793042115501134

start page

• 2431

end page

• 2450

volume

• 11

issue

• 8

URL

• http://dx.doi.org/10.1142/s1793042115501134