Le probl\`eme des diviseurs pour des formes binaires de degr\'e 4

TL;DR

This paper investigates the average behavior of the divisor function when applied to values of reducible binary quartic forms, contributing to understanding their arithmetic properties.

Contribution

It provides new insights into the divisor function's average order over reducible binary quartic forms, a previously less-explored area.

Findings

Determined the average order of the divisor function for reducible binary quartic forms.

Established asymptotic formulas for the divisor function over these forms.

Enhanced understanding of the distribution of divisors in algebraic forms.

Abstract

We study the average order of the divisor function, as it ranges over the values of binary quartic forms that are reducible over the rationals.