An Investigation Into Several Explicit Versions of Burgess' Bound

Abstract

Let $\chi$ be a Dirichlet character modulo $p$, a prime. In applications, one often needs estimates for short sums involving $\chi$. One such estimate is the family of bounds known as \emph{Burgess' bound}. In this paper, we explore several minor adjustments one can make to the work of Enrique Treviño on explicit versions of Burgess' bound. For an application, we investigate the problem of the existence of a $k$th power non-residue modulo $p$ which is less than $p^{\alpha }$ for several fixed $\alpha$. We also provide a quick improvement to the conductor bounds for norm-Euclidean cyclic fields.

14 pages, version 2

Cited by in corpus (1)

• Explicit Improvements to the Burgess Bound Via Pólya-Vinogradov