The frequency and the structure of large character sums

Jonathan Bober, Leo Goldmakher, Andrew Granville +1

Let $M(\chi )$ denote the maximum of $|{\sum }_{n\le N}\chi (n)|$ for a given non-principal Dirichlet character $\chi (\mathrm{mod}q)$, and let $N_{\chi }$ denote a point at which the maximum is attained. In t…