Grayson Plumpton (Queen's University)
Date
Monday February 13, 20234:30 pm - 5:30 pm
Location
Jeffery Hall, Room 319Number Theory Seminar
Monday, February 13th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Grayson Plumpton (Queen's University)
Title: An idelic approach to probability laws related to the Riemann zeta function
Abstract: In a 1999 paper by Biane, Pitman, and Yor, they construct a random variable whose expectation is related to Riemann's xi function. Using this, they give a probabilistic interpretation of the first two Li coefficients appearing in Li's criterion for the Riemann hypothesis. They take a classical approach, making use of Jacobi's theta function, which is at times messy and not easily generalizable to other Dedekind zeta functions. In this talk I discuss how one might reapproach this result by considering random variables on the idele group of a number field.