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 square-root 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 square-root 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
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