# Computing zeta functions of generic projective hypersurfaces in larger characteristic

## TL;DR

This paper improves the deformation method for calculating zeta functions of generic projective hypersurfaces in characteristic p, significantly reducing the dependence on p for both time and space complexities.

## Contribution

It introduces enhanced deformation techniques that lower the complexity dependence on p, making computations more efficient for larger characteristic fields.

## Key findings

- Reduced time complexity dependence to p^{1/2}
- Reduced space complexity dependence to log(p)
- Maintains polynomial complexity in other parameters

## Abstract

We give improvements of the deformation method for computing the zeta function of a generic projective hypersurface in characteristic~$p$ that either reduce the dependence on~$p$ of the time complexity to $\tilde{O}(p^{1/2})$ or that of the space complexity to $\tilde{O}(\log(p))$ while remaining polynomial in the other input parameters.