RAMANUJAN DUALS AND AUTOMORPHIC SPECTRUM

被引：39

作者：

BURGER, M

LI, JS

SARNAK, P

机构：

[1] UNIV MARYLAND,DEPT MATH,COLLEGE PK,MD 20742

[2] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544

[3] IBM CORP,ALMADEN RES CTR,DIV RES,SAN JOSE,CA 95120

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 26卷 / 02期

关键词：

D O I：

10.1090/S0273-0979-1992-00267-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of the automorphic dual of a matrix algebraic group defined over Q . This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic functorial properties of this set are derived and used both to deduce arithmetic vanishing theorems of "Ramanujan" type as well as to give a new construction of automorphic forms.

引用

页码：253 / 257

页数：5

共 23 条

[1]

BOREL A., 1980, ANN MATH STUD, V94

[2]

Borel A., 1963, TOPOLOGY, V2, P111, DOI 10.1016/0040-9383(63)90026-0

[3] RAMANUJAN DUALS .2. [J].

BURGER, M ;

SARNAK, P .

INVENTIONES MATHEMATICAE, 1991, 106 (01) :1-11

[4]

COWLING M, 1988, J REINE ANGEW MATH, V387, P97

[5] LIMIT FORMULAS FOR MULTIPLICITIES IN L2(GAMMA-G) [J].

DEGEORGE, DL ;

WALLACH, NR .

ANNALS OF MATHEMATICS, 1978, 107 (01) :133-150

[6]

DIXMIER J, 1977, C STAR ALGEBRAS

[7] KLOOSTERMAN SUMS FOR CLIFFORD ALGEBRAS AND A LOWER BOUND FOR THE POSITIVE EIGENVALUES OF THE LAPLACIAN FOR CONGRUENCE SUBGROUPS ACTING ON HYPERBOLIC SPACES [J].

ELSTRODT, J ;

GRUNEWALD, F ;

MENNICKE, J .

INVENTIONES MATHEMATICAE, 1990, 101 (03) :641-685

[8]

FARAUT J, 1979, J MATH PURE APPL, V58, P369

[9]

GELBART SS, 1978, ANN SCI ECOLE NORM S, V2, P471

[10]

Gelfand I.M, 1969, REPRESENTATION THEOR

← 1 2 3 →