Dorian Goldfeld, Ph.D.

Dorian Goldfeld is a professor of mathematics at Columbia University. Goldfeld’s research interests include various topics in number theory. In his thesis, he proved a version of Artin’s conjecture on primitive roots on the average without the use of the Riemann hypothesis.

In 1976, Goldfeld provided the key ingredient for the effective solution of Gauss’ class number problem for imaginary quadratic fields. Specifically, he proved an effective lower bound for the class number of an imaginary quadratic field assuming the existence of an elliptic curve whose L-function had a zero of order at least 3 at s=1/2 (such a curve was found soon after by Gross and Zagier). This effective lower bound then allows the determination of all imaginary fields with a given class number after a finite number of computations.

Goldfeld received his B.S. degree in 1967 from Columbia University. He is the recipient of the Frank Nelson Cole Prize in Number Theory for his solution of Gauss’ class number problem for imaginary quadratic fields as well as the Vaughan Prize. He has been an invited speaker at the International Congress of Mathematicians in Berkeley and is a fellow of the American Academy of Arts and Sciences and a fellow of the American Mathematical Society