Short Character Sums and the Pólya–Vinogradov Inequality
(2022)
Journal Article
Mangerel, A. P. (2022). Short Character Sums and the Pólya–Vinogradov Inequality. The Quarterly Journal of Mathematics, 71(4), 1281–1308. https://doi.org/10.1093/qmath/haaa031
We show in a quantitative way that any odd primitive character χ modulo q of fixed order g ≥ 2 satisfies the property that if the Pólya–Vinogradov inequality for χ can be improved to max1≤t≤q∣∣∣∣∑n≤tχ(n)∣∣∣∣=oq→∞(q√logq) then for any ɛ > 0 one may ex... Read More about Short Character Sums and the Pólya–Vinogradov Inequality.