Dan Goldston

Dan Goldston (1984)

Daniel Alan "Dan" Goldston (born January 4, 1954 in Oakland , California ) is an American mathematician who deals with analytical number theory.

life and career

Goldston grew up in Piedmont , California and studied from 1971 at the Massachusetts Institute of Technology and at the University of California, Berkeley , where he earned his bachelor's degree in 1975 and his master's degree in 1978 and his doctorate in 1981 with RS Lehman. In 1981 he was Assistant Professor at the University of Minnesota (Duluth) and at the Institute for Advanced Study (1982/83, also 1990). He has been at San José State University since 1983 , where he has been associate professor since 1985 and professor of mathematics since 1988. He was visiting scholar at the University of Toronto (1994, with John Friedlander ) and at MSRI (1999).

Goldston became known for a sentence related to the twin prime conjecture. With Cem Yıldırım and János Pintz in 2005, after his first proof with Yıldırım was incorrect and was withdrawn, he proved that the following is asymptotical for the distances between consecutive prime numbers:

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

In other words, for each there is a pair of consecutive prime numbers p and p 'with ${\displaystyle c>0}$

${\displaystyle |p-p'|<c\cdot \log p}$.

The three mathematicians were jointly awarded the Cole Prize for Number Theory in 2014. In 2014 he was invited speaker with Pintz and Yildirim at the ICM in Seoul (Small gaps between primes).

Web links

• Dan Goldston's homepage

Individual evidence

1. ^ Daniel Alan Goldston, Yoichi Motohashi, János Pintz, Cem Yalçın Yıldırım: Small gaps between primes exist. In: Proceedings of the Japan Academy. Series A: Mathematical Sciences. Vol. 82, No. 4, 2006, pp. 61-65, ( online ).