Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

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Abstract

We prove multiplicative relations between certain Fourier coefficients of degree 2 Siegel eigenforms. These relations are analogous to those for elliptic eigenforms. We also provide two sets of formulas for the eigenvalues of degree 2 Siegel eigenforms. The first evaluates the eigenvalues in terms of the form's Fourier coefficients, in the case a(I)≠0. The second expresses the eigenvalues of index p and p2, for p prime, solely in terms of p and k, the weight of the form, in the case a(0)≠0. From this latter case, we give simple expressions for the eigenvalues associated to degree 2 Siegel Eisenstein series.

Original languageEnglish
Pages (from-to)263-281
Number of pages19
JournalJournal of Number Theory
Volume170
DOIs
StatePublished - Jan 1 2017

Keywords

  • Fourier coefficients
  • Hecke eigenvalues
  • Siegel modular forms

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