Automorphic Forms, Representation, and L-functions
File : pdf, 25 MB, 322 pages
CONTENTS
I Reductive groups, Representations
Reductive groups
Reductive groups over local fields
Representation of reductive Lie groups
Representations of GL2(R) and GL2(C)
Normalizing factors, tempered representation, an L-groups
Orbital integrals for GL2(R)
Representations of -adic groups: A survey
Cuspidal unramified series for central simple algebras over local fields
Some remarks on the supercuspidal representatinos of p-adic semisimple groups
II Automorphic forms and representations
Decomposition of representation into tensor products
Classical and adelic automorphic forms. An introduction
Automorphic forms and automorphic representation
On the notion of an automorphic representation.
Multiplicity one theorems
Forms of GL(2) from the analytic point of vies
Einstein series and the trace formula
0-series and invariant theory
Examlples of dual reductive pairs
On a relation between SL2 cusp forms and automorphic forms on orthogonal groups
A counterexample to the “generalized Ramanujan conjecture” for (quasi-) split groups
II Automorphic representation and L-functions
Number theoretic background
Automorphic L-functions
Principal L-functions of the linear group
Automorphic L-functions for the symplectic group GSp4
On liftings of holomorphic cusp forms
Orbital integrals and base change
The solution of a base change problem for GL(2)
Report on the local Langlands conjecture for GL2
IV Arithmetical algebraic geometry and automorphic L-functions
The Hasse-Weil function of some moduli varieties of dimension greater than one
Points on Shimura varieties amod p
Combinatories and Shimura varieties mod p
Notes on L-indistinguishablility
Automorphic representation, Shimura varieties, and motives
Congruence relations and Shimura curves
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