Education
University of California, Berkeley.
mathematician university professor
University of California, Berkeley.
He is currently a professor of mathematics at San Jose State University. He has an Erdos number of 2. Goldston is best known for the following result that he, János Pintz, and Cem Yıldırım proved in 2005:
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, id est (that is)
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.