TY - JOUR
T1 - Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms
AU - McCarthy, Dermot
N1 - Funding Information:
This work was supported by a grant from the Simons Foundation (# 353329 , Dermot McCarthy).
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
AB - 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.
KW - Fourier coefficients
KW - Hecke eigenvalues
KW - Siegel modular forms
UR - http://www.scopus.com/inward/record.url?scp=84981344725&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2016.06.022
DO - 10.1016/j.jnt.2016.06.022
M3 - Article
AN - SCOPUS:84981344725
VL - 170
SP - 263
EP - 281
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -