Mathematics Department Colloquium
The Mathematics Department Colloquium meets periodically throughout the academic year.
Latest colloquium information for the 2012-2013 academic year:
Department of Mathematics
University Tennessee at Chattanooga
Thursday, April 11, EMCS 422, 3:00-3:50 pm.
Differences between consecutive primes
Abstract. In 1976, Gallagher proved that the Hardy-Littlewood prime k-tuple conjecture implies that, for the primes up to x, the number of primes in the interval (x, x + \lambda \log x] follows a Poisson distribution with mean \lambda, where \lambda is any fixed positive constant. Very recently, Professor Daniel A. Goldston (San Jose State University) and I proved that the number of consecutive primes with difference \lambda \log x has the Poisson distribution superimposed on the conjectured asymptotic formula for pairs of primes with this difference. In this talk, I will present an extension of Gallagher's theorem and more precise asymptotic formulas if \lambda approaches zero as x tends to infinity. In order to establish these asymptotic formulas, we also proved new singular series average results.
This talk is appropriate for all students with an interest in number theory.