Daniel Goldston

Daniel Goldston
Born	(1954-01-04) January 4, 1954 Oakland, California
Nationality	American
Alma mater	UC Berkeley
Known for	GPY theorem in number theory
Awards	Cole Prize (2014)
Scientific career
Fields	Mathematics
Institutions	San Jose State University
Thesis	Large differences between consecutive prime numbers  (1981)
Doctoral advisor	Russell Lehman

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.

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

$\liminf _{n\to \infty }{\frac {p_{n+1}-p_{n}}{\log p_{n}}}=0$

where $p_{n}$ denotes the n^th 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}\$.

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.

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.

See also

• Landau's problems
• Yitang Zhang
• James Maynard (mathematician)

External links

• Dan Goldston's Homepage