Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
manuscripta math. 104, 173 200 (2001) Springer-Verlag 2001 Mahdi Asgari Ralf Schmidt
 

Summary: manuscripta math. 104, 173 200 (2001) Springer-Verlag 2001
Mahdi Asgari Ralf Schmidt
Siegel modular forms and representations
Received: 28 March 2000 / Revised version: 25 October 2000
Abstract. This paper explicitly describes the procedure of associating an automorphic rep-
resentation of PGSp(2n, A) with a Siegel modular form of degree n for the full modular
group n = Sp(2n, Z), generalizing the well-known procedure for n = 1. This will show
that the so-called "standard" and "spinor" L-functions associated with such forms are ob-
tained as Langlands L-functions. The theory of Euler products, developed by Langlands,
applied to a Levi subgroup of the exceptional group of type F4, is then used to establish
meromorphic continuation for the spinor L-function when n = 3.
1. Introduction
Let f be a Siegel modular form of degree n for the full modular group n =
Sp(2n, Z). If f is an eigenfunction for the action of the Hecke algebra, then there
are two L-functions associated with f . Let a0, a1, . . . , an be the Satake parameters
of f , and define the standard L-function
L1(s, f ) =
p
(1 - p-s
)

  

Source: Asgari, Mahdi - Department of Mathematics, Oklahoma State University

 

Collections: Mathematics