# A Heat Equation on some Adic Completions of Q and Ultrametric Analysis

## TL;DR

This paper introduces a new geometrical approach to analyze a heat equation on ultrametric groups formed by p-adic fields, providing a general framework for such problems.

## Contribution

It develops a simple, geometrical method for studying heat equations on ultrametric groups like Q_S, expanding the analytical toolkit beyond traditional techniques.

## Key findings

- Established a new framework for heat equations on ultrametric groups
- Provided a general approach applicable to various ultrametric structures
- Simplified analysis using geometrical methods

## Abstract

This article deals with a Markov process related to the fundamental solution of a heat equation on the direct product ring Q_S, where Q_S is a finite direct product of p-adic fields. The techniques developed here are different from the well known ones: they are geometrical and very simple. As a result, the techniques developed here provides a general framework of these problems on other related ultrametric groups.