# Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

## TL;DR

This paper establishes conditions under which monomial deformations of Delsarte hypersurfaces in weighted projective spaces share common factors in their zeta functions, extending previous specific cases to more general scenarios.

## Contribution

It provides a general criterion for common factors in zeta functions of monomial deformations of Delsarte hypersurfaces, broadening earlier results.

## Key findings

- Identified sufficient conditions for shared zeta function factors.
- Extended previous specific cases to more general hypersurfaces.
- Found that the common factors can be of higher degree than previously known.

## Abstract

Let $X_\lambda$ and $X_\lambda'$ be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results by Doran, Kelly, Salerno, Sperber, Voight and Whitcher [arXiv:1612.09249], where they showed this for a particular monomial deformation of a Calabi-Yau invertible polynomial. It turns out that our factor can be of higher degree than the factor found in [arXiv:1612.09249].