Rigidity in automorphic representations and local systems

Automorphic Representations with Local Constraints

To everyone who loves mathematics, everywhere. i Acknowledgements I cannot stress enough how wonderful it is to study mathematics at Berkeley. I had the great privilege to share ideas there with many fantastic mathematicians. My advisor, Ken Ribet, granted me the freedom to pursue this project while masterfully answering the lion's share of my questions. The ideas for the final chapter grew out...

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...

Automorphic Representations and L-functions

• Decomposition by central characters • Square-integrable cuspforms • Smoothness of cuspforms • Eigen-cuspforms and automorphic representation • Dirichlet series versus zeta and L-functions • L-functions defined via local data • Factoring unitary representations of adele groups • Spherical representations and Satake parameters • Local data, L-groups, higher L-functions References and historical...