Mean values of divisors twisted by quadratic characters

TL;DR

This paper evaluates a sum involving quadratic characters and the divisor function, providing insights into the behavior of these number-theoretic functions and their interactions.

Contribution

It introduces a new evaluation of a sum involving Kronecker symbols and divisor functions, advancing understanding of twisted mean values in number theory.

Findings

Explicit formula for the sum involving quadratic characters and divisors

New bounds or asymptotics for the sum

Insights into the distribution of quadratic residues

Abstract

In this paper, we evaluate the sum $\sum_{m,n}\leg {m}{n}d(n)$, where $\leg {m}{n}$ is the Kronecker symbol and $d(n)$ is the divisor function.