Central morphisms and cuspidal automorphic representations

Two Dimensional Adelic Analysis and Cuspidal Automorphic Representations of Gl(2)

Two dimensional adelic objects were introduced by I. Fesenko in his study of the Hasse zeta function associated to a regular model E of the elliptic curve E. The Hasse-Weil L-function L(E, s) of E appears in the denominator of the Hasse zeta function of E . The two dimensional adelic analysis predicts that the integrand h of the boundary term of the two dimensional zeta integral attached to E i...

On tensor product $L$-functions and Langlands functoriality

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

Introduction to Automorphic Representations

L-Functions and Automorphic Representations*

There are two kinds of L-functions, and they will be described below: motivic L-functions which generalize the Artin L-functions and are defined purely arithmetically, and automorphic L-functions, defined by data which are largely transcendental. Within the automorphic L-functions a special class can be singled out, the class of standard L-functions, which generalize the Hecke L-functions and f...

Automorphic Representations and Number Theory *

An excellent introduction to the theory of automorphic representations and the relations with number theory is the Corvallis proceedings, Automorphic Forms, Representations and L-Functions, Parts 1 and 2, Proc. Sympos. Pure Math., vol. 33, 1979. Although composed mainly of survey articles, the proceedings are already rather formidable. They are a measure of the breadth of the field. They will b...