Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

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• 作者：Dermot McCarthy ^{dermot.mccarthy@ttu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11F30 ; 11F46
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：263-281
• 全文大小：375 K

文摘

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 formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301731&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301731&_rdoc=1&_issn=0022314X&md5=2d7de01245c4ed1514f1cd6117513624" title="Click to view the MathML source">a(I)≠0$a(I)\ne 0$. The second expresses the eigenvalues of index p   and formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301731&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301731&_rdoc=1&_issn=0022314X&md5=abcb1a344fcefebf0609e70126b02a3c" title="Click to view the MathML source">p²$p^2$, for p prime, solely in terms of p and k  , the weight of the form, in the case formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301731&_mathId=si3.gif&_user=111111111&_pii=S0022314X16301731&_rdoc=1&_issn=0022314X&md5=a0e4fb917233f3ba55033f99cb844e37" title="Click to view the MathML source">a(0)≠0$a(0)\ne 0$. From this latter case, we give simple expressions for the eigenvalues associated to degree 2 Siegel Eisenstein series.