A note on mass equidistribution of holomorphic Siegel modular forms

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• 作者：Sheng-Chi Liu ^{scliu@math.wsu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11F11 ; 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：185-190
• 全文大小：251 K

文摘

Let 72X&_mathId=si1.gif&_user=111111111&_pii=S0022314X1630172X&_rdoc=1&_issn=0022314X&md5=6d1ee85e86958b1af9d9bc351bcb9e97" title="Click to view the MathML source">F_f∈S_k(Sp_2n(Z))$F_f\in S_k({\mathit{Sp}}_{2n}(\mathbb{Z}))$ be the Ikeda lifting of a Hecke eigenform 72X&_mathId=si2.gif&_user=111111111&_pii=S0022314X1630172X&_rdoc=1&_issn=0022314X&md5=de50eb9b7d2157433faaa8a5bc259e32" title="Click to view the MathML source">f∈S_2k−n(SL₂(Z))$f\in S_{2k-n}({\mathit{SL}}_2(\mathbb{Z}))$ with the normalization 72X&_mathId=si3.gif&_user=111111111&_pii=S0022314X1630172X&_rdoc=1&_issn=0022314X&md5=b085bb03163375a8f64a127572b3a707" title="Click to view the MathML source">〈F_f,F_f〉=1$〈F_f,F_f〉=1$. Let 72X&_mathId=si4.gif&_user=111111111&_pii=S0022314X1630172X&_rdoc=1&_issn=0022314X&md5=3bdc385f6b6abc428ccef26234542b41" title="Click to view the MathML source">E(Z;s)$E(Z;s)$ denote the Klingen Eisenstein series. In this paper we verify that which is predicted by the mass equidistribution conjecture of Cogdell and Luo [CL].