On restricted divisor sums associated to the Chowla-Walum conjecture

TL;DR

This paper investigates restricted divisor sums related to the Chowla-Walum conjecture, improving estimates, extending the conjecture, and deriving generalized asymptotic formulas for these sums.

Contribution

It provides new bounds on restricted divisor sums, extends the Chowla-Walum conjecture, and generalizes asymptotic formulas for these sums.

Findings

Improved estimate for mean value of restricted divisor sums

Extended the Chowla-Walum conjecture to restricted ranges

Derived generalized asymptotic formulas

Abstract

We first study the mean value of certain restricted divisor sums involving the Chowla-Walum sums, improving in particular a recent estimate given by Iannucci. The aim of the second part of this work is the generalization of the previous study, by restricting the range of the divisors in the studied divisor sums, extending the Chowla-Walum conjecture, proving a small part of this extended conjecture and generalizing the asymptotic formulas previously obtained in the first part.