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 curriculum vitae
Some Preprints: (pdf files)
A standard zero free region for Rankin-Selberg L-functions (with X. Li)
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
 
                    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 2015

Mathematics W4007,  ANALYTIC NUMBER THEORY
 TR 2:40am-3:55pm Location: Room 528 Mathematics Building

Textbooks: Multiplicative Number Theory (Harold Davenport)
                     A Course in Arithmetic (J.P. Serre)
 
TA:
Joćo Guerreiro
e-mail: guerreiro@math.columbia.edu
Help Room Hours: 1 - 4 p.m. on Mondays (Room 406 Math Building)

HOMEWORK: 

Homework #1 (due Thursday, Feb. 12)
Homework #2 (due Thursday, Feb. 26)
Homework #3 (due Thursday, March 12)
Homework #4 (due Thursday, April 16)

FINAL EXAM (due 12:00 noon, Sunday, May 3)


RESEARCH SEMINAR-NUMBER THEORY
Location: 528 Mathematics Building
TUESDAY  11:40a.m. - 12:55p.m.

Feb. 3:        Ali Altuğ (A brief introduction to functoriality and beyond endoscopy)
Feb. 10:      Ali Altuğ (A brief introduction to functoriality and beyond endoscopy)
Feb. 17:      Joćo Guerreiro (An application of the GL(3) Kuznetsov trace formula)
Feb. 24:      Wong Tian An (Zeroes of L-functions in the GL(2) trace formula)
March 3:     Vivek Pal (The Hasse principle for K3 surfaces)
March 10:   Vladislov Petkov (A converse theorem for metaplectic Eisenstein series for SL(2))
March 17:   Spring Break
March 24:   Zheng Liu
March 31:   Zheng Liu
April 7:       Shrenik Shah
April 14:     Shrenik Shah
April 21:     Xin Wan
April 28:     Xin Wan