Multiplicative relations for Fourier coefficients of degree 2 Siegel\n eigenforms

2015/05/26 by Dermot McCarthy, McCarthy, Dermot
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1505.07049

openalex publication_date 2015/05/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We prove multiplicative relations between certain Fourier coefficients of\ndegree 2 Siegel eigenforms. These relations are analogous to those for elliptic\neigenforms. We also provide two sets of formulas for the eigenvalues of degree\n2 Siegel eigenforms. The first evaluates the eigenvalues in terms of the form's\nFourier coefficients, in the case a(I) \≠ 0. The second expresses the\neigenvalues of index p and p², for p prime, solely in terms of p and\nk, the weight of the form, in the case a(0)\≠ 0. From this latter case,\nwe give simple expressions for the eigenvalues associated to degree 2 Siegel\nEisenstein series.\n

Related

• Some relations on Fourier coefficients of degree 2 Siegel forms of\n arbitrary level
• Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences
• Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series
• Recursion formulas for the Fourier coefficients of Siegel Eisenstein series of an odd prime level
• On Fourier coefficients and Hecke eigenvalues of Siegel cusp forms of degree 2