The distribution of primes in short intervals.

Abstract: What is the maximum number of primes in an interval of length $y$? Here $y$ is no bigger than a small multiple of $(\log x)^2$, that is, $y$ is tiny compared to $x$. We will present several conjectures (for different ranges of $y$) based on (a couple of) heuristic ideas, and investigate these conjectures with data from calculations of primes. There are one or two surprising issues that arise. This is joint work with Allysa Lumley.

algebraic geometrynumber theory

Audience: researchers in the topic

MAGIC (Michigan - Arithmetic Geometry Initiative - Columbia)

Series comments: Description: Research seminar in arithmetic geometry

(Zoom password = order of the alternating group on six letters)