On approximation of p-adic numbers by p-adic algebraic numbers

TL;DR

This paper proves a comprehensive Khintchine type theorem in the p-adic setting, characterizing how well p-adic algebraic numbers can approximate p-adic numbers.

Contribution

It establishes the first complete p-adic Khintchine theorem for approximation by p-adic algebraic numbers, filling a key gap in number theory.

Findings

Complete p-adic Khintchine theorem proved

Characterization of approximation quality in p-adic numbers

Advances understanding of p-adic algebraic approximation

Abstract

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.