An observation on generalized Hilbert-Kunz functions

TL;DR

This paper shows that, under specific conditions, generalized Hilbert-Kunz multiplicities can be represented as linear combinations of the classical Hilbert-Kunz multiplicities, providing a new perspective on their structure.

Contribution

It introduces a method to express generalized Hilbert-Kunz multiplicities as linear combinations of classical ones under certain assumptions.

Findings

Generalized Hilbert-Kunz multiplicities can be expressed as linear combinations of classical multiplicities.

The paper establishes conditions under which this linear relationship holds.

This provides a new approach to understanding the structure of Hilbert-Kunz functions.

Abstract

We prove that, under certain assumptions, generalized Hilbert-Kunz multiplicities can be expressed as linear combinations of classical Hilbert-Kunz multiplicities.