Averages of arithmetic functions over principal ideals

TL;DR

This paper establishes upper bounds for the averages of a broad class of non-negative arithmetic functions over principal ideals linked to irreducible binary forms with integer coefficients in number fields.

Contribution

It introduces new upper bounds for averages of arithmetic functions over principal ideals associated with irreducible binary forms in number fields.

Findings

Upper bounds for averages of arithmetic functions over principal ideals.

Application to irreducible binary forms with integer coefficients.

Generalization to a broad class of non-negative functions.

Abstract

For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with integer coefficients.