Local theory of primitive theta functions

被引：11

作者：

Murase, A ^{[1
]}

Sugano, T

机构：

[1] Kyoto Sangyo Univ, Fac Sci, Dept Math, Kita Ku, Kyoto 6038555, Japan

[2] Kanazawa Univ, Fac Sci, Dept Math, Kanazawa, Ishikawa 9201192, Japan

来源：

COMPOSITIO MATHEMATICA | 2000年 / 123卷 / 03期

关键词：

theta function; Heisenberg group; metaplectic representation;

D O I：

10.1023/A:1002051017269

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U}(1)).

引用

页码：273 / 302

页数：30

共 13 条

[1]

[Anonymous], 1998, NUMBER THEORY TIRUCH, DOI DOI 10.1090/CONM/210/02790

[2] FUNCTIONAL-EQUATION OF ARTIN L-FUNCTION FOR CHARACTERS OF REAL REPRESENTATIONS [J].

FROHLICH, A ;

QUEYRUT, J .

INVENTIONES MATHEMATICAE, 1973, 20 (02) :125-138

[3]

GLAUBERMAN GI, 1989, J REINE ANGEW MATH, V395, P68

[4] Theta dichotomy for unitary groups [J].

Harris, M ;

Kudla, SS ;

Sweet, WJ .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (04) :941-1004

[5] CHARACTER OF WEILS REPRESENTATION [J].

HOWE, RE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 177 (MAR) :287-298

[6]

KATO Y, 1980, THESIS U TOKYO

[7]

Moeglin C., 1987, LECT NOTES MATH, V1291

[8] THE DUAL PAIR (U(1), U(1)) OVER A P-ADIC FIELD [J].

MOEN, C .

PACIFIC JOURNAL OF MATHEMATICS, 1993, 158 (02) :365-386

[9]

Rogawski J., 1992, ZETA FUNCTIONS PICAR, P395

[10]

SHINTANI T, 1979, UNPUB AUTOMORPHIC FO

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