Open Access

On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues

Research in Number Theory20162:10

DOI: 10.1007/s40993-015-0034-2

Received: 5 October 2015

Accepted: 27 December 2015

Published: 15 February 2016

Abstract

We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.

Keywords

Drinfeld-Goss modular forms Hecke operators Eigenform coefficients Difference operators