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
                    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, FALL 2012

Mathematics V3025,  MAKING, BREAKING CODES
Day/Time: TR 2:40pm-3:55pm Location: 312 Mathematics Building

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


TA's: Tim Heath  <timheath@math.columbia.edu>  Help Room Hours: 1-4 Wednesdays
           Luis Garcia  <lgarcia@math.columbia.edu>   Help Room Hours: Mondays 12-1 and Fridays 1-2pm
 
EXAM 1:
Thursday, October 4  (20% of total grade for this course)
        

EXAM 2:  Thursday, November 8   (20% of total grade for this course)
                                  
FINAL EXAM:  Thursday, December 20 (1:10-4:00p.m. in Room 312)   (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 11:59pm. All homework is from the Trappe-Washington book.

HW#1 due Thursday, September 13:   Page 55, Problems 2, 3, 4, 5, 8, 10, 11
HW#2 due Thursday, September 20:   Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26
HW#3 due  Thursday, September 27:   Page 192, Problems 1, 3, 7, 9, 11  Page 214, Problems 1, 2, 11
HW#4 due Thursday, October 11:   Page 105, Problems 9, 10  Page 195, Problem 21  Page 215, Problems 3, 4, 6, 10
HW#5 due Thursday, October 18:   Page 108, Problems 25, 26,  Page 239, Problems 1, 2, 3, 4,  Page 252, Problem 1
HW#6 due Thursday, October 25:   Page 252, Problems 2, 4, 5, 8,  Page 286, Problem 4,   Page 315, Problems 2, 3.
HW#7 due Thursday, November 1:   Page 370, Problems 1, 2, 3, 4, 5, 10
HW#8 due Thursday, November 8:   Page 321, Problems 1, 2, 3, 4, 5, 6
HW#9 due Thursday, November 15:   Page 110, Problems 33, 34,  Page 447,  Problem 12(a),  Construct a finite field of 8 elements.
HW#10 due Thursday, November 29:   Page 445, Problems 1,  2,  3(a),(b),(c),  4,  5(a),  6
HW#11 due Thursday, December 6:   Page 445, Problems 8, 9, 10, 11, 12, 13




Mathematics W4043,  ALGEBRAIC NUMBER THEORY
Day/Time: TR 11:40am-12:55pm Location: 507 Mathematics Building

Textbook: Algebraic Number Theory, by Jurgen Neukirch, Grundlehren der mathematischen Wissenschaften 322, Springer

TA: Nava Balsam  <nava@math.columbia.edu>
  Help Room Hours: Tuesday 10-12 and Wednesdays 12-1pm

HOMEWORK:  (60% of total grade for this course)
Please put all homework in the box just opposite Room 414 Math Building.
Deadline is Thursday 11:59pm. All homework is from the Neukirch book.

HW#1 due Thursday, September 13:  Page 5, Problems 1, 2, 5, 6, 7.
HW#2 due Thursday, September 27:  Page 15, Problems 1, 2, 4, 5,   Page 23, Problems 1,2
HW#3 due Thursday, October 11:   Page 23, Problems 3, 4, 5, 6
HW#4 due Thursday, October 25:   Page 27, Problems 1, 3,  Page 38, Problem 1,  Page 43, Problems 1, 2
HW#5 due Thursday, December 6:   Page 58, Problems 1, 2, 3, 4