Grayson Plumpton (Queen's University)
Date
Tuesday November 21, 20234:00 pm - 5:00 pm
Location
Jeffery Hall, Room 319Number Theory Seminar
Tuesday, November 21st, 2023
Time: 4:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Grayson Plumpton (Queen's University)
Title: Some probability laws concerning the Dedekind zeta functions of $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.
Abstract: This talk is a follow up to a talk given at the number theory seminar in winter 2023, in which we introduce the paper 鈥淧robability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions鈥 by Phillipe Biane, Jim Pitman, and Marc Yor. In this talk, we will reframe some ideas from this paper using the language of Tate-Iwasawa theory, and use this to give a probabilistic interpretation of the Dedekind zeta functions of the fields $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.