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)
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:
                    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
            

TEACHING, FALL 2014

Mathematics W3025,  MAKING, BREAKING CODES
 TR 2:40am-3:55pm Location: Room 312 Mathematics Building

Textbook: Introduction to Cryptography with Coding Theory (Second Edition)
                    by Wade Trappe and Lawrence Washington.
 
TA's:

Pak-Hin Lee <phlee@math.columbia.edu>  Help Room Hours: 3-6 on Mondays.
Tim Heath <timheath@math.columbia.edu>  Help Room Hours: 9-11 on Tuesdays.
Riaz Ayub Helfer <rah2181@columbia.edu>  Help Room Hours: 12-1 Wed. Thurs.

Exam1:  Thursday, Oct. 2 
(20% of total grade for this course)

Exam2:  Thursday, Nov. 6  (20% of total grade for this course)

FINAL EXAM:  Thursday, Dec. 18 from 1:10p.m - 4:00p.m.   (35% of total grade for this course)

HOMEWORK:  (25% of total grade for this course)
Please put all homework in the box near Room 417 Math Building. 
Deadline is Thursday 11:59pm. All homework is from the Trappe-Washington book.

HW#1 due Thursday, September 11:   Page 55, Problems 2, 3, 4, 5, 8, 10, 11
HW#2 due Thursday, September 18:   Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26
HW#3 due  Thursday, September 25:   Page 192, Problems 1, 3, 7, 9, 11  Page 214, Problems 1, 2, 11
HW#4 due Thursday, October 2:   Page 105, Problems 9, 10  Page 195, Problem 21  Page 215, Problems 3, 4, 6, 10
HW#5 due Thursday, October 9:   Page 108, Problems 25, 26,  Page 239, Problems 1, 2, 3, 4
HW#6 due Thursday, October 16:   Page 252, Problems 1, 2, 4, 5, 8,  Page 286, Problem 4,   Page 315, Problems 2, 3
HW#7 due Thursday, October 23:   Page 370, Problems 1, 2, 3, 4, 5, 10
HW#8 due Thursday, October 30:   Page 321, Problems 1, 2, 3, 4, 5, 6
HW#9 due Thursday, November 6:   Page 110, Problems 33, 34,  Page 447,  Problem 12(a),  Construct a finite field of 8 elements.
HW#10 due Thursday, November 13:   Page 445, Problems 1,  2,  3(a),(b),(c)
HW#11 due Thursday, November 20:   Page 445, Problems  4,  5(a),(b),  6, 8
HW#12 due Thursday, December 4:   Page 445, Problems  9, 10, 11, 12, 13