The divisor problem for binary cubic forms

TL;DR

This paper studies the average behavior of the divisor function when applied to values of totally reducible binary cubic forms, providing insights and potential applications in number theory.

Contribution

It introduces new results on the divisor problem specifically for binary cubic forms and explores their implications.

Findings

Derived asymptotic formulas for divisor sums over binary cubic forms

Identified applications in related number theoretic problems

Extended understanding of divisor distribution in algebraic forms

Abstract

We investigate the average order of the divisor function at values of totally reducible binary cubic forms and discuss some applications.