Mathematics Building, Room 422
Columbia University
New York, NY 10027 
(212) 854-4304
       Fax: (212) 854-8962


Research Interests:  Number Theory curriculum vitae
Some Preprints: (pdf files)
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 


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
                    L-functions and Automorphic forms (Goldfeld Fest)     (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


 TR 11:40am-12:55pm Location:  Mathematics Building

Textbook: Multiplicative Number Theory (Second Edition)
                    by Harold Davenport, GTM 74, Springer.

TA's: Vladislov Petkov  

FINAL EXAM:  Wednesday, May 14, 2014,  9:00a.m. - 12:00 noon  (35% of total grade for this course)

HOMEWORK:  (65% of total grade for this course)
Please put all homework in the box just opposite Room 417 Math Building.

HW#1-due Thursday, February 6, 2014

HW#2-due Thursday, February 27, 2014

HW#3-due Tuesday, March 25, 2014

HW#4-due Thursday, May 8, 2014