Quadratic character sums with multiplicative coefficients

TL;DR

This paper investigates the extreme values of quadratic character sums with multiplicative coefficients, employing the resonance method to establish conditional lower bounds within a specific range of N.

Contribution

It introduces a new application of the resonance method to quadratic character sums with multiplicative coefficients, providing conditional Omega-results.

Findings

Established conditional lower bounds for quadratic character sums

Applied the resonance method in a novel context

Identified extremal behavior of these sums within certain ranges

Abstract

In this article, we study extreme values of quadratic character sums with multiplicative coefficients $\sum_{n \le N}f(n)\chi_d(n)$. For a positive number $N$ within a suitable range, we employ the resonance method to establish a conditional $\Omega$-result.