A Vorono\"i--Oppenheim summation formula for number fields

TL;DR

This paper derives a Voronoi--Oppenheim summation formula for divisor functions over any number field, extending classical results to a broader algebraic setting.

Contribution

It introduces a generalized summation formula for divisor functions in the context of arbitrary number fields, expanding the scope of classical analytic number theory tools.

Findings

Established a Voronoi--Oppenheim summation formula for number fields

Extended classical divisor function analysis to algebraic number fields

Provided a new analytical tool for number theory over number fields

Abstract

In this note, we establish a Vorono\"i--Oppenheim summation formula for divisor functions over an arbitrary number field.