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)
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        

                    Links:
                    L-functions and Automorphic forms (Goldfeld Fest)     (Conference photos)
                    Automorphic Forms and L-Functions for the Group GL(n,R)
                    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
                    Very accurate clock
            

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TEACHING:
Spring 2010 - Making, breaking codes, Math V3025
Tuesday/Thursday: 2:40 - 3:55 p.m.   
Location: 312 Mathematics Building
Lecturer (Dorian Goldfeld),  Office Hours: by appointment only
TA's: Min Lee:   http://math.columbia.edu/~enoia/
           Daniel Disegni:   http://www.math.columbia.edu/~disegni/
HelpRoom Hour: Mondays, 11:00-12:00 a.m. in Room 307
Book: Introduction to cryptography with coding theory (2nd edition by Trappe-Washington)

Exam 1: Thursday, March 4 in class
Exam 2: Thursday, April 8 in class
Final Exam: TBA
Makeup exams will be given only under exceptional circumstances and need a note from a doctor or a dean.
Please bring ID to the tests.

Grading: Exams 1, 2 (40%),  Final exam (35%),  Homework (25%).

Weekly Homework (all problems taken from the book Introduction to Cryptography by Trappe-Washington)
Please put homework in Box on 4th floor of Math Building (midnight on Thursday is the deadline):

due Thursday, Jan 28:  p. 55:  problems  5, 7, 8, 10, 11
due Thursday, Feb. 4:  p. 104: problems 1, 2, 4, 7, 8, 9, 12, 13
due Thursday, Feb. 11:  p. 192: problems 1, 2, 3, 4, 7, 9, 12, 16