New equidistribution estimatesof Zhang type Page 1 Algebra & Number Theory msp Volume 8
2014 No. 9 New equidistribution estimates of Zhang type DHJ Polymath Page 2 msp ALGEBRA …

Let $ p_n $ denote the $ n $ th prime. We prove that\[\max _ {p_ {n}\leqslant X}(p_ {n+ 1}-
p_n)\gg\frac {\log X\log\log X\log\log\log\log X}{\log\log\log X}\] for sufficiently large $ X …

Using geometric methods, we improve on the function field version of the Burgess bound
and show that, when restricted to certain special subspaces, the Möbius function over F_qT …

Modern neural networks obtain information about the problem and calculate the output
solely from the input values. We argue that it is not always optimal, and the network's …

Large gaps between primes Page 1 Annals of Mathematics 183 (2016), 915-933 http://dx.doi.Org/10.4007/annals.2016.183.3.3
Large gaps between primes By James Maynard Abstract We show that there exist pairs of …

The infamous twin prime conjecture states that there are infinitely many pairs of distinct
primes which differ by $2 $. Until recently this conjecture had seemed to be far out of reach …

Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of
complete complementary codes (CCCs), which enables multicarrier communication systems …

For any $ m\geq 1$, let $ H_m $ denote the quantity $ H_m:=\liminf_ {n\to\infty}(p_ {n+ m}-
p_n) $, where $ p_n $ denotes the $ n^{\operatorname {th}} $ prime; thus for instance the …

This book came out of an attempt to explain to a class of motivated students at the University
of Illinois at Chicago what sorts of problems I thought about in my research. In the course, we …

Abstract The Twin Prime Conjecture asserts that there should be infinitely many pairs of
primes which differ by 2. Unfortunately this long-standing conjecture remains open, but …