On the representations generated by Eisenstein series of weight n+3/2

被引：1
|
作者：
Horinaga, Shuji [1 ]
机构：
[1] Kyoto Univ, Grad Sch Math, Kyoto 6068502, Japan
来源：
JOURNAL OF NUMBER THEORY | 2019年 / 201卷
关键词：
Siegel modular forms; Nearly holomorphic modular forms; Eisenstein series; Automorphic forms;
D O I：
10.1016/j.jnt.2019.02.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Eisenstein series E(z, s; k, chi, N) of weight k = (n + 3)/2, level N > 1 and a Dirichlet character chi modulo N such that chi(2) = 1. Shimura proved that E(z, k/2; k, chi, N) is a nearly holomorphic function. We prove that E(z, k/2; k, chi, N) generates an indecomposable reducible (g, K)-module of length 2. These are new examples of indecomposable reducible (g, K)-modules generated by nearly holomorphic modular forms. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：206 / 227
页数：22
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