Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two

被引：4

作者：

Gun, Sanoli ^{[1
]}

Kohnen, Winfried ^{[2
]}

Paul, Biplab ^{[3
]}

机构：

[1] Homi Bhabha Natl Inst, Inst Math Sci, CIT Campus, Chennai 600113, Tamil Nadu, India

[2] Heidelberg Univ, Math Inst, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[3] Kyushu Univ, Fac Math, Nishi Ku, 744 Motooka, Fukuoka 8190395, Japan

来源：

RAMANUJAN JOURNAL | 2021年 / 54卷 / 01期

关键词：

Siegel modular forms; Hecke eigenvalues; Multiplicity one theorem; Simultaneous non-vanishing; MODULAR-FORMS;

D O I：

10.1007/s11139-020-00254-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F and G be Siegel cusp forms for Sp(4)(Z) and weights k(1), k(2), respectively. Also let F and G be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither F nor G is a Saito-Kurokawa lift. In this article, we study simultaneous arithmetic behaviour of Hecke eigenvalues of these Hecke eigenforms.

引用

页码：43 / 62

页数：20

共 16 条

[1]

Andrianov A., 1974, Russian Math Surveys, V29, P45

[2]

Bocherer S., 1986, Mathematica Gottingensis, Gttingen, V68, P36

[3] On Hecke eigenforms in the Maass space [J].

Breulmann, S .

MATHEMATISCHE ZEITSCHRIFT, 1999, 232 (03) :527-530

[4] On a convolution series attached to a Siegel Hecke cusp form of degree 2 [J].

Das, Soumya ;

Kohnen, Winfried ;

Sengupta, Jyoti .

RAMANUJAN JOURNAL, 2014, 33 (03) :367-378

[5] On Hecke eigenvalues of Siegel modular forms in the Maass space [J].

Gun, Sanoli ;

Paul, Biplab ;

Sengupta, Jyoti .

FORUM MATHEMATICUM, 2018, 30 (03) :775-783

[6]

Gun S, 2016, J RAMANUJAN MATH SOC, V31, P125

[7] A NOTE ON EIGENVALUES OF HECKE OPERATORS ON SIEGEL MODULAR-FORMS OF DEGREE 2 [J].

KOHNEN, W .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 113 (03) :639-642

[8] Sign changes of Hecke eigenvalues [J].

Matomaki, Kaisa ;

Radziwill, Maksym .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2015, 25 (06) :1937-1955

[9] ON THE POLES OF ANDRIANOV L-FUNCTIONS [J].

ODA, T .

MATHEMATISCHE ANNALEN, 1981, 256 (03) :323-340

[10] Transfer of Siegel Cusp Forms of Degree 2 [J].

Pitale, Ameya ;

Saha, Abhishek ;

Schmidt, Ralf .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 232 (1090) :1-+

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