On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

被引：3

作者：

Chida, Masataka ^{[1
]}

Katsurada, Hidenori ^{[2
]}

Matsumoto, Kohji ^{[3
]}

机构：

[1] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto 6068502, Japan

[2] Muroran Inst Technol, Muroran, Hokkaido 0508585, Japan

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG | 2014年 / 84卷 / 01期

关键词：

Siegel modular form; Fourier coefficients; Petersson formula; AUTOMORPHIC L-FUNCTIONS;

D O I：

10.1007/s12188-013-0087-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a formula of Petersson's type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficients. The method in this paper is essentially a generalization of Kitaoka's previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.

引用

页码：31 / 47

页数：17

共 8 条

[1] UBER HILBERT-SIEGELSCHE MODULFORMEN UND POINCARESCHE REIHEN [J].

CHRISTIAN, U .

MATHEMATISCHE ANNALEN, 1962, 148 (04) :257-307

[2] THE CRITICAL ORDER OF VANISHING OF AUTOMORPHIC L-FUNCTIONS WITH LARGE LEVEL [J].

DUKE, W .

INVENTIONES MATHEMATICAE, 1995, 119 (01) :165-174

[3]

Hua L. K., 1982, INTRO NUMBER THEORY

[4]

Iwaniec H., 1997, Topics in classical automorphic forms, DOI DOI 10.1090/GSM/017

[5] Certain mean values and non-vanishing of automorphic L-functions with large level [J].

Kamiya, Y .

ACTA ARITHMETICA, 2000, 93 (02) :157-176

[6] FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE-2 [J].

KITAOKA, Y .

NAGOYA MATHEMATICAL JOURNAL, 1984, 93 (MAR) :149-171

[7]

Klingen H, 1990, Cambridge Studies in Advanced Mathematics, V20

[8] Local spectral equidistribution for Siegel modular forms and applications [J].

Kowalski, Emmanuel ;

Saha, Abhishek ;

Tsimerman, Jacob .

COMPOSITIO MATHEMATICA, 2012, 148 (02) :335-384

← 1 →