Daniel Goldston

Daniel Goldston
Born	January 4, 1954 Oakland, California
Nationality	American
Fields	Mathematics
Institutions	San Jose State University
Alma mater	UC Berkeley
Doctoral advisor	Russell Lehman
Known for	GPY theorem in number theory
Notable awards	Cole Prize (2014)

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. He has an Erdős number of 2.

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

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

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}\$.

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.

See also

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

References

1. http://arxiv.org/abs/math/0508185
2. http://aimath.org/primegaps/
3. http://www.aimath.org/primegaps/residueerror/

External links

• Dan Goldston's Homepage