# Exponential Sums of Witt Towers over Affinoids

## TL;DR

This paper develops a Dwork theory for exponential sums over affinoids in Witt towers, enabling the computation of L-function degrees and analysis of Hodge and Newton polygons.

## Contribution

It introduces a novel Dwork theory framework for exponential sums over affinoids in Witt towers, advancing understanding of their L-functions and polygon relations.

## Key findings

- Computed the degree of the L-function.
- Analyzed the Hodge polygon.
- Identified conditions for Hodge and Newton polygons to coincide.

## Abstract

In this paper we construct a Dwork theory for general exponential sums over affinoids in Witt towers. Using this, we compute the degree of the $L$-function, its Hodge polygon and examine when the Hodge and Newton polygons coincide.