Squared Mobius function for half-integral matrices and its applications

被引：6

作者：

Ibukiyama, T ^{[1
]}

Katsurada, H ^{[1
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Osaka 5600043, Japan

来源：

JOURNAL OF NUMBER THEORY | 2001年 / 86卷 / 01期

关键词：

D O I：

10.1006/jnth.2000.2568

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define an analogue of the square of the usual Mobius function on the set of non-degenerate half-integral matrices. By using this function, we give a reasonable expression of the Koecher-MaaB Dirichlet series for a Siegel Modular form. In addition, we give another proof to a main result of (T. Ibukiyama and H. Saito, 1995, Amer. J. Math. 117, 1097-1155) oil the zeta functions for symmetric matrices. (C) 2001 Academic Press.

引用

页码：78 / 117

页数：40

共 12 条

[1]

BOCHERER S, 1985, J REINE ANGEW MATH, V362, P146

[2]

BOCHERER S, 1988, J REINE ANGEW MATH, V384, P80

[3] SUMS INVOLVING VALUES AT NEGATIVE INTEGERS OF L-FUNCTIONS OF QUADRATIC CHARACTERS [J].

COHEN, H .

MATHEMATISCHE ANNALEN, 1975, 217 (03) :271-285

[4] ON ZETA-FUNCTIONS ASSOCIATED TO SYMMETRICAL MATRICES .1. AN EXPLICIT FORM OF ZETA-FUNCTIONS [J].

IBUKIYAMA, T ;

SAITO, H .

AMERICAN JOURNAL OF MATHEMATICS, 1995, 117 (05) :1097-1155

[5] A NOTE ON LOCAL-DENSITIES OF QUADRATIC-FORMS [J].

KITAOKA, Y .

NAGOYA MATHEMATICAL JOURNAL, 1983, 92 (DEC) :145-152

[6] EULER PRODUCTS AND FOURIER COEFFICIENTS OF AUTOMORPHIC-FORMS ON SYMPLECTIC GROUPS [J].

SHIMURA, G .

INVENTIONES MATHEMATICAE, 1994, 116 (1-3) :531-576

[7] On the theory of indefinite quadratic forms [J].

Siegel, CL .

ANNALS OF MATHEMATICS, 1944, 45 :577-622

[8] The analytical theory of quadratic forms [J].

Siegel, CL .

ANNALS OF MATHEMATICS, 1935, 36 :527-606

[9] 2-ADIC DENSITY OF A QUADRATIC FORM [J].

WATSON, GL .

MATHEMATIKA, 1976, 23 (45) :94-106

[10]

[No title captured]

← 1 2 →