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)   
                    Links:
                    L-functions and Automorphic forms (Goldfeld Fest)     (Conference photos)

                    Joint COLUMBIA-CUNY-NYU Number Theory Seminar
                    Braid Group Cryptography
                    Bretton Woods Workshop on Multiple Dirichlet Series(2005)    (Conference photos)
                    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 2012

Mathematics V3025,  MAKING, BREAKING CODES
Day/Time: TR 11:00am-12:15pm Location: 203 Mathematics Building

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


TA's:
Luis Garcia:
  lgarcia@math.columbia.edu
                                 Help Room: Math 406 on Mondays 10-11am and Tuesdays 4-6pm
Tim Heath:    timheath@math.columbia.edu
                                 Help Room: Math 406 on Wednesdays 1-4pm

EXAM 1:
Thursday, February 16  (20% of total grade for this course)
        
Exam1a-Solutions          Exam1b-Solutions
EXAM 2:  Thursday, March 29   (20% of total grade for this course)
                                    Exam2-Solutions
FINAL EXAM:  Tuesday, May 8,  9:00a.m. - 12:00p.m.   (35% of total grade for this course)

HOMEWORK:  (25% of total grade for this course)
Please put all homework in the box just opposite Room 414 Math Building.
Deadline is Thursday 12:00 midnight. All homework is from the Trappe-Washington book.

HW#1 due Thursday, January 26:   Page 55, Problems 2, 3, 4, 5, 8, 10, 11
HW#2 due Thursday, February 2:   Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26
HW#3 due Thursday, February 9:   Page 192, Problems 1, 3, 7, 9, 11  Page 214, Problems 1, 2, 11
HW#4 due Thursday, February 16:   Page 105, Problems 9, 10  Page 195, Problem 21  Page 215, Problems 3, 4, 6, 10
HW#5 due Thursday, March 1:   Page 108, Problems 25, 26,  Page 239, Problems 1, 2, 3, 4,  Page 252, Problem 1
HW#6 due Thursday, March 8:   Page 252, Problems 2, 4, 5, 8,  Page 286, Problem 4,   Page 315, Problems 2, 3.
HW#7 due Thursday, March 22:   Page 370, Problems 1, 2, 3, 4, 5, 10
HW#8 due Thursday, March 29:   Page 321, Problems 1, 2, 3, 4, 5, 6
HW#9 due Thursday, April 12:   Page 110, Problems 33, 34,  Page 447,  Problem 12(a),  Construct a finite field of 8 elements.
HW#10 due Thursday, April 19:   Page 445, Problems 1, 2, 3, 4, 5, 6
HW#11 due Thursday, April 26:   Page 445, Problems 8, 9, 10, 11, 12, 13




Mathematics W4007,  ANALYTIC NUMBER THEORY
Day/Time: TR 2:40-3:55pm Location: 307 Mathematics Building

Homework #1
Homework #2
Homework #3