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Daniel Goldston

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Nationality  American
Role  Mathematician
Alma mater  UC Berkeley
Fields  Mathematics
Doctoral advisor  Russell Lehman
Notable awards  Cole Prize
Name  Daniel Goldston

Daniel Goldston httpsuploadwikimediaorgwikipediacommonsthu

Born  January 4, 1954 (age 62)Oakland, California (1954-01-04)
Institutions  San Jose State University
Known for  GPY theorem in number theory
Education  University of California, Berkeley

A conversation between yitang zhang and daniel goldston


Daniel Alan Goldston (born January 4, 1954 in Oakland, California) is an American mathematician who specializes in number theory. He is currently a professor of mathematics at San Jose State University.

Daniel Goldston ZALA films Counting from Infinity

Goldston is best known for the following result that he, János Pintz, and Cem Yıldırım proved in 2005:

Daniel Goldston Prime Numbers Progress and Pitfalls YouTube
lim inf n p n + 1 p n log p n = 0
Daniel Goldston A conversation between Yitang Zhang and Daniel Goldston HD 2013

where p n denotes the nth prime number. In other words, for every c > 0   , there exist infinitely many pairs of consecutive primes p n   and p n + 1   which are closer to each other than the average distance between consecutive primes by a factor of c   , i.e., p n + 1 p n < c log p n   .

Daniel Goldston Home Page

This result was originally reported in 2003 by Goldston and Yıldırım but was later retracted. Then Pintz joined the team and they completed the proof in 2005.

Daniel Goldston Dan Goldstons Website About Me

In fact, if they assume the Elliott–Halberstam conjecture, then they can also show that primes within 16 of each other occur infinitely often, which is related to the twin prime conjecture.

Daniel Goldston Faculty Alphabetical Department of Mathematics Statistics

References

Daniel Goldston Wikipedia