Roger Baker

Affiliation: Brigham Young University

Email: baker@math.byu.edu

Title Of Talk: Limit points and long gaps between primes

Abstract:

Let $d_n$ denote the nth prime gap. Recent progress in the study of normalized prime gaps has led to the conclusion that the sequence $d_n/f(n)$ has limit points occupying at least 25% of the positive real line, if $f(n)$ is a well-behaved function that grows to infinity no faster than $R(n) =\log n \log_2(n) \log_4(n)/ (\log_3(n))^2$. This is due to Pintz, building on work of Banks,Freiberg and Maynard. The speaker and Tristan Freiberg have obtained the corresponding result with $R(n)$ replaced by any well-behaved function growing slower than $R(n)$ $\log _3(n)$, the function occurring in the recent gap result of Ford, Green, Konyagin, Maynard and Tao. Our work draws on the techniques in the three works cited above, especially the last one. The talk covers some indications of these techniques .