## DORIAN GOLDFELD

Professor

Mathematics Building, Room 422

Columbia University

New York, NY 10027(212) 854-4304

Telephone:

Fax:(212) 854-8962

e-mail:goldfeld@columbia.edu

Research Interests:Number Theory curriculum vitae

Some Preprints: (pdf files)

An additive prime divisor function of Alladi and Erdős

A standard zero free region for Rankin-Selberg L-functions (with X. Li)

A converse theorem for double Dirichlet series and Shintani zeta functions

(with N. Diamantis)

On the determination of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)

(with A. Kontorovich)

Fourier expansions of GL(2) newforms at various cusps

(with J. Hundley and M. Lee)

Natural boundaries and the correct notion of integral moments of L-functions

(with A. Diaconu and P. Garrett)

Moments for L-functions for GL(r) x GL(r-1) (with A. Diaconu and P. Garrett)

A converse theorem for double Dirichlet series (with N. Diamantis)

Voronoi Formulas on GL(n) (with X. Li)

Second Moments of GL(2) L-Functions (with A. Diaconu)

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

BOOKS:

Automorphic Representations and L-Functions for the General Linear Group, Volume 1

Automorphic Representations and L-Functions for the General Linear Group, Volume 2

Automorphic Forms and L-Functions for the Group GL(n,R)

Blog with corrections of Errors in the above books

UPCOMING CONFERENCES:

First JNT Biennial Conference (July 22 - 26, 2019)

Links:

(Goldfeld Conference photos)

Joint COLUMBIA-CUNY-NYU Number Theory Seminar

Bretton Woods Workshop on Multiple Dirichlet Series(2005) (Conference photos)

AAG key exchange

Edinburgh Workshop on Multiple Dirichlet Series(2008)

Decision Regarding World Record Musky Challenge

My Daughter's art work (including my portrait above)

Some Interesting Chemistry

Very accurate clock

TEACHING, SPRING 2018

Mathematics GR8674, TOPICS IN ANALYTIC NUMBER THEORY

TR 1:10 - 2:25 Location: Room 507 Mathematics Building

RECOMMENDED (not required) Textbooks:

Automorphic forms and L-functions for the group GL(n, R), by D. Goldfeld

Cambridge University Press (2015).

This course will focus on recent developments in the spectral theory of automorphic forms

on GL(n,R) with n > 2. I will begin by reviewing the basic theory of automorphic forms

and L-functions on the upper half plane H^n. One of the main goals is to present new

methods to derive the Fourier expansion of Langlands Eisenstein series twisted by cusp

forms of lower rank and then obtain spectral expansions of L^2 automorphic forms into

cusp forms, Langlands Eisenstein series, and residues of Langlands Eisenstein series. We

will then give applications that have been developed recently to the trace formula, spectral

reciprocity, special values of L-functions, and other topics.