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

Masataka Chida; Hidenori Katsurada; Kohji Matsumoto

doi:10.1007/s12188-013-0087-x

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

Masataka Chida, Hidenori Katsurada, Kohji Matsumoto

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	31-47
Number of pages	17
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	84
Issue number	1
DOIs	https://doi.org/10.1007/s12188-013-0087-x
Publication status	Published - 2014 Apr

Keywords

Fourier coefficients
Petersson formula
Siegel modular form

ASJC Scopus subject areas

Mathematics(all)

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abstract = "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.",

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AU - Chida, Masataka

AU - Katsurada, Hidenori

AU - Matsumoto, Kohji

PY - 2014/4

Y1 - 2014/4

N2 - 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.

AB - 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.

KW - Fourier coefficients

KW - Petersson formula

KW - Siegel modular form

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JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

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IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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