## DORIAN GOLDFELD

Professor

Mathematics Building, Room 422

Columbia University

New York, NY 10027(212) 854-4304

Telephone:

Fax:(212) 854-8962

e-mail:goldfeld@columbia.edu

Research Interests:Number Theory curriculum vitae

Some Preprints: (pdf files)A standard zero free region for Rankin-Selberg L-functions (with X. Li)

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 2015

Mathematics V3027, 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 C. Washington, Prentice Hall

TA: Joćo Guerreiro

e-mail:guerreiro@math.columbia.edu

Help Room Hours:Tuesdays:10am -11:30am,Thursdays:1pm - 2:30pm

TA: Paul Lewis

e-mail:pdlewis@math.columbia.edu

Help Room Hours:Wednesdays: 11am - 2pm

EXAM 1:Thursday, October 8(20% of total grade for this course)

EXAM 2:Thursday, November 12(20% of total grade for this course)

Projected FINAL EXAM:Thursday, December 17: 1:10-4pm(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 417 Math Building.

Deadline is Thursday 11:59pm. All homework is from the Trappe-Washington book.

HW#1 due Thursday, September 17: Page 55, Problems 2, 3, 4, 5, 8, 10, 11

HW#2 due Thursday, September 24: Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26

HW#3 due Thursday, October 1: Page 192, Problems 1, 3, 7, 9, 11 Page 214, Problems 1, 2, 11

HW#4 due Thursday, October 8: Page 105, Problems 9, 10 Page 195, Problem 21 Page 215, Problems 3, 4, 6, 10

HW#5 due Thursday, October 15: Page 108, Problems 25, 26, Page 239, Problems 1, 2, 3, 4

HW#6 due Thursday, October 22: Page 252, Problems 1, 2, 4, 5, 8, Page 286, Problem 4, Page 315, Problems 2, 3

HW#7 due Thursday, October 29: Page 321, Problems 1, 2, 3, 4, 5, 6

HW#8 due Thursday, November 5: Page 370, Problems 1, 2, 3, 4, 5, 10

HW#9 due Thursday, November 12: Page 110, Problems 33, 34, Page 447, Problem 12(a), Construct a finite field of 8 elements.

HW#10 due Thursday, November 19: Page 445, Problems 1, 2, 3(a),(b),(c)

HW#11 due Thursday, December 3: Page 445, Problems 4, 5(a),(b), 6, 8

HW#12 due Thursday, December 10: Page 445, Problems 9, 10, 11, 12, 13

RESEARCH SEMINAR-NUMBER THEORY

Mathematics G9905

Location:507 Mathematics Building

TUESDAYS 11:40a.m. - 12:55p.m.

DATE

SPEAKER

TITLE

September 22

Wei Zhang Super-positivity of L-functions September 29

David Soudry

On local descent of supercuspidal representations

from GL(n) to classical groups

October 6

Ioan Filip A local relative trace formula for spherical varieties and distinguished representations

October 13 Tian An Wong

Explicit formulas via trace formulas

October 20 Daniel Litt

Hyperbolicity of moduli spaces and function field arithmetic

October 27 Ali Altug

Trace formula, analytic number theory, and related problems November 3

Election Day - - University Holiday

November 10 Rahul Krishna

A new relative trace formula approach to Waldspurger's formula for toric periods

November 17 Joćo Guerreiro

The classical and adelic versions of the GL(3) Kuznetsov trace formula

November 24 Bingrong Huang

Hybrid sup-norm bounds for Eisenstein series

December 1 Vivek Pal

Mazur-Tate conjecture