School Seminars and Colloquia

Gaps between Primes in an Arithmetic Progression

Pure Mathematics Seminar

by Liangyi Zhao


Institution: UNSW
Date: Fri 13th October 2017
Time: 3:15 PM
Location: Peter Hall 213

Abstract: Let $t$ be a natural number. We show that there are infinitely many t-tuples of primes $p_1<⋯ \[ p_t–p_1\ll q \exp(Bt). \]
Here the value of $B$ depends on $q$. The proof uses the methods in the breakthrough of J. Maynard on the small gaps between primes as well as other inputs from the study of the (possible) Siegel zeros of Dirichlet $L$-functions. This is joint work with R. C. Baker. This talk is intended for a general mathematical audience and technical details of the work will be kept at a minimum.