Dorian Goldfeld
| Dorian M. Goldfeld | |
|---|---|
Dorian Goldfeld at The Analytic Theory of Automorphic Forms workshop, Oberwolfach, Germany (2011)
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| Born |
January 21, 1947 Marburg, Germany |
| Nationality | American |
| Fields | Mathematics |
| Institutions |
Columbia University Massachusetts Institute of Technology |
| Alma mater | Columbia University |
| Doctoral advisor | Patrick X. Gallagher |
| Doctoral students |
Jeffrey Hoffstein M. Ram Murty Eric Stade |
| Known for | Number Theory, Cryptography |
| Notable awards |
Frank Nelson Cole Prize in Number Theory (1987) Sloan Fellowship (1977–1979) Vaughan prize (1985) Fellow of the American Academy of Arts and Sciences (April 2009) |
Dorian Morris Goldfeld (born January 21, 1947) is an American mathematician.
He received his B.S. degree in 1967 from Columbia University. His doctoral dissertation, entitled "Some Methods of Averaging in the Analytical Theory of Numbers", was completed under the supervision of Patrick X. Gallagher in 1969, also at Columbia. He has held positions at the University of California at Berkeley (Miller Fellow, 1969–1971), Hebrew University (1971–1972), Tel Aviv University (1972–1973), Institute for Advanced Study (1973–1974), in Italy (1974–1976), at MIT (1976–1982), University of Texas at Austin (1983–1985) and Harvard (1982–1985). Since 1985, he has been a professor at Columbia University.
He is a member of the editorial board of Acta Arithmetica and of The Ramanujan Journal.
He is a co-founder and board member of SecureRF, a corporation that has developed the world’s first linear-based security solutions.
Dorian 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 an 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.
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