Large values of quadratic character sums revisited

TL;DR

This paper investigates large quadratic character sums for lengths exceeding the square root of the modulus, providing new Omega results under the Generalized Riemann Hypothesis.

Contribution

It offers new lower bounds (Omega results) for quadratic character sums beyond the square root length, assuming GRH, advancing understanding of their extremal behavior.

Findings

Established new Omega bounds under GRH

Extended the analysis of quadratic character sums to longer lengths

Provided theoretical insights into the extremal values of these sums

Abstract

We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omega result.