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)
An additive prime divisor function of Alladi and Erdős
A standard zero free region for Rankin-Selberg L-functions (with X. Li)

A converse theorem for double Dirichlet series and Shintani zeta functions
                                                   (with N. Diamantis)
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:
                    (Goldfeld 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 2017

Mathematics
V3025,  MAKING, BREAKING CODES
  TR 2:40-3:55  Location: Room 312 Mathematics Building

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

TA:  James Cornish
e-mail:  jsc2219@columbia.edu     

Help Room (Math 406) Hours: 
Wed. 12-1, Thurs. 1-3.

Midterm Exam1  Tuesday October 3  (20% of total grade for this class)

Midterm Exam2  TBA (20% of total grade for this class)

Final Exam  TBA (35% of total grade for this class)

Homework (25% of total grade for this course) 
Please put all homework in the box just opposite Room 415 Math Building.
Deadline is Thursday 11:00pm (Note that Math Building is locked by Facilities at 11:00pm).
All homework is from the Trappe-Washington book.

HW#1 due Thursday, September 14:   Page 55, Problems 2, 3, 4, 5, 8, 10, 11

HW#2 due Thursday, September 21:   Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26

HW#3 due  Thursday, September 28:  Page 105, Problems 9, 10  Page 192, Problems 1, 3, 7, 9   Page 214, Problems 1, 2, 11