Arithmeticity of holomorphic cuspforms on Hermitian symmetric domains

被引：1

作者：

Lanphier, Dominic ^{[1
]}

Urtis, Cetin ^{[2
]}

机构：

[1] Western Kentucky Univ, Dept Math, Bowling Green, KY 42101 USA

[2] TOBB Econ & Technol Univ, Dept Math, TR-06560 Ankara, Turkey

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 151卷

关键词：

Cuspforms; Siegel Eisenstein series; Siegel-Weil Eisenstein series; Theta series; SIEGEL-WEIL FORMULA; EISENSTEIN SERIES; MODULAR-FORMS; UNITARY GROUPS; INNER PRODUCTS; ZETA-FUNCTIONS; SPECIAL VALUES; CUSPIDALITY; PULLBACKS;

D O I：

10.1016/j.jnt.2014.12.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove Galois equivariance of ratios of Petersson inner products of holomorphic cuspforms on symplectic, unitary, or Hermitian orthogonal groups. As a consequence, we show that the ratios of Petersson norms of such cuspforms with the same Hecke eigenvalues are algebraic. We also show that spaces of such cuspforms of sufficiently high fixed weight and level are spanned by theta series. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：230 / 262

页数：33

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