Intersective polynomials and Diophantine approximation, II

TL;DR

This paper uses Schmidt's lattice method to establish results on simultaneous Diophantine approximation modulo 1 for polynomial systems in a prime variable, under specific local conditions.

Contribution

It extends Diophantine approximation results to polynomial systems in prime variables using lattice techniques and local conditions.

Findings

Proves new bounds for Diophantine approximation in prime variables

Establishes conditions under which simultaneous approximation is possible

Extends previous work on polynomial Diophantine approximation

Abstract

By applying Schmidt's lattice method, we prove results on simultaneous Diophantine approximation modulo 1 for systems of polynomials in a single prime variable provided that certain local conditions are met.