Character Studies

: Investigating the Limiting Distribution of Character Sums

Abstract

Dirichlet characters, and their partial sums, play a fundamental role in analytic number theory. In this thesis, we study various distributions of these character sums and find the limiting distribution as the conductor tends to infinity. We consider the limit of two main distributions: the continuous paths of character sums modulo a prime q on the complex plane, and partial sums of quadratic characters with prime conductors in the dyadic range [Q, 2Q] for some Q > 0. The limiting distributions are formulated as Fourier series with Steinhaus and Rademacher random multiplicative functions as the respective Fourier coefficients.

Date of Award	21 Jun 2022
Original language	English
Awarding Institution	University of Bristol
Supervisor	Jonathan W Bober (Supervisor)