A rank computation problem related to the HK function of trinomial hypersurfaces

TL;DR

This paper solves a rank computation problem crucial for determining the Hilbert-Kunz function of disjoint-term trinomial hypersurfaces over fields of characteristic 2, enabling formula derivation for these functions.

Contribution

It provides a novel solution to a previously posed rank computation problem, facilitating the calculation of the Hilbert-Kunz function for specific hypersurfaces.

Findings

Rank computation method for disjoint-term trinomial hypersurfaces

Explicit formula derivable for Hilbert-Kunz function

Applicable over any field of characteristic 2

Abstract

In this article, I provide a solution to a rank computation problem related to the computation of the Hilbert-Kunz function for any disjoint-term trinomial hypersurface, over any field of characteristic 2. This rank computation problem was posed in Upadhyay (arXiv:1204.5417). The formula for the Hilbert-Kunz function for disjoint-term trinomial hypersurfaces can be deduced from the result(s) of this article, modulo a lot of tedious notation.