Video library: A. Harper, The distribution of short moving character sums

VIDEO LIBRARY


Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov September 13, 2021 16:30, Moscow, Steklov Mathematical Institute, 8, Gubkina str, room 110 + online

The distribution of short moving character sums A. Harper University of Warwick, Mathematics Institute
Abstract: Sums of Dirichlet characters are one of the most studied objects in analytic number theory. In this talk I will describe some work on the distribution of $$ \sum\limits_{x\,<\,n\,\leqslant\,x+H}\chi(n), $$ where $\chi$ is a non-principal character $\mod{q}$ and $x$ varies between $0$ and $q-1$. This problem was investigated by Davenport and Erdös, and more recently by Lamzouri and others. Lamzouri conjectured that provided $$ H\to\infty, \quad\text{but}\quad H = o\left(\frac{q}{\log{q}}\right), $$ the sum should have a Gaussian limiting distribution. I will present some results that shed more light on this conjecture.