 
Summary: manuscripta math. 104, 173 200 (2001) © SpringerVerlag 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 wellknown procedure for n = 1. This will show
that the socalled "standard" and "spinor" Lfunctions associated with such forms are ob
tained as Langlands Lfunctions. 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 Lfunction 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 Lfunctions associated with f . Let a0, a1, . . . , an be the Satake parameters
of f , and define the standard Lfunction
L1(s, f ) =
p
(1  ps
)
