Gauss and p-adic numbers
Number Theory
2025-10-14 v1 History and Overview
Abstract
In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of in the -adic integers in order to find an -adic approximation to a quadratic Gauss sum, computes a nontrivial square root of in -adic integers, and computes the -adic logarithms of small natural numbers.
Keywords
Cite
@article{arxiv.2510.11559,
title = {Gauss and p-adic numbers},
author = {Franz Lemmermeyer},
journal= {arXiv preprint arXiv:2510.11559},
year = {2025}
}