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On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues

Research in Number Theory20162:10

https://doi.org/10.1007/s40993-015-0034-2

  • Received: 5 October 2015
  • Accepted: 27 December 2015
  • Published:

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

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