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
Born (1954-01-04) January 4, 1954
NationalityAmerican
Alma materUC Berkeley
Known forGPY theorem in number theory
AwardsCole Prize (2014)
Scientific career
FieldsMathematics
InstitutionsSan Jose State University
ThesisLarge differences between consecutive prime numbers (1981)
Doctoral advisorRussell Lehman
InfluencedYitang Zhang

Research

Goldston is best known for the following result that he, János Pintz, and Cem Yıldırım proved in 2005:[1]

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

This result was originally reported in 2003 by Goldston and Yıldırım but was later retracted.[2][3] Then Pintz joined the team and they completed the proof in 2005.

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.

Recognition

Goldston was named to the 2021 class of fellows of the American Mathematical Society "for contributions to analytic number theory".[4]

See also

References

  1. Goldston, D. A.; Pintz, J.; Yildirim, C. Y. (2005). "Primes in Tuples I". arXiv:math/0508185.
  2. http://aimath.org/primegaps/
  3. "Archived copy". Archived from the original on 2009-02-20. Retrieved 2009-03-31.CS1 maint: archived copy as title (link)
  4. 2021 Class of Fellows of the AMS, American Mathematical Society, retrieved 2020-11-02
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