Date: Friday, January 07, 2022
Location: Virtual (4:00 PM to 5:00 PM)
Title: Odd moments in the distribution of primes
Abstract: In 2004, Montgomery and Soundararajan showed (conditionally) that the distribution of the number of primes in appropriately sized intervals is approximately Gaussian and has a somewhat smaller variance than you might expect from modeling the primes as a purely random sequence. Their work depends on evaluating sums of certain arithmetic constants that generalize the twin prime constant, known as singular series. In particular, these sums exhibit squareroot cancellation in each term if they have an even number of terms, but if they have an odd number of terms, there should be slightly more than squareroot cancellation. I will discuss sums of singular series with an odd number of terms, including tighter bounds for small cases and the function field analog. I will also explain how this problem is connected to a simple problem about adding fractions.
Files:
Speaker: Vivian Kuperberg
Institution: Stanford University
Event Organizer: Kartik Prasanna
