DORIAN GOLDFELD

Professor        Mathematics Building, Room 422        Columbia University        New York, NY 10027               Telephone: (212) 854-4304        Fax: (212) 854-8962        e-mail: goldfeld@columbia.edu

Research Interests:  Number Theory

Recent Preprints: (pdf files)
Voronoi Formulas on GL(n) (with X. Li) new
Second Moments of GL(2) L-Functions (with A. Diaconu) new
Counting Congruence Subgroups (with A. Lubotzky and L. Pyber)
Multiple Dirichlet Series and Moments of Zeta and L-Functions
                                                 (with A. Diaconu and J. Hoffstein)
Modular Forms, Elliptic Curves, and the ABC Conjecture
The Gauss Class Number problem for Imaginary Quadratic Fields
The Elementary proof of the Prime Number Theorem,  An Historical Perspective

          

                    Links
                    
                    L-functions and Automorphic forms (Goldfeld Fest)     (conference photos)
                    
                    Automorphic Forms and L-Functions for the Group GL(n,R) (Just published!)

                    Joint COLUMBIA-CUNY-NYU Number Theory Seminar
                                      
                    Braid Group Cryptography

                    Bretton Woods Workshop on Multiple Dirichlet Series

                    Decision Regarding World Record Musky Challenge

                    Very accurate clock



            

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Teaching, FALL 2008:

MATH G6659 Automorphic Representations 4.5 pts.
(Tuesday/Thursday 11:00-12:15, Room 307 Math Building)

FIRST MEETING: Tuesday, September 9, 2008

This course is part of the NSF funded Research Training Group
in Number Theory (RTG) held jointly by COLUMBIA-CUNY-NYU.

COURSE DESCRIPTION

This course presents the Jacquet-Langlands theory of automorphic representations for GL(2). The stress will be to develop the theory with many concrete explicit examples. Topics to be covered include: Fourier analysis on the adele group, the classical theory of automorphic forms for GL(2), automorphic forms on the adele group, automorphic representations, Whittaker functions,  local theory - principal series representations, special representations, (g, K)-modules, the supercuspidal representations, tensor products of local representations, L-functions, Godement-Jacquet proof of the analytic continuation and functional equation of L-functions.