A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1

TL;DR

This paper introduces a purely combinatorial method to study simultaneous polynomial recurrence modulo 1, providing new insights into Diophantine approximation for systems of polynomials with real coefficients.

Contribution

It presents a novel combinatorial approach to analyze polynomial recurrence modulo 1, expanding the tools available for Diophantine approximation problems.

Findings

Results on simultaneous Diophantine approximation modulo 1

New combinatorial techniques for polynomial recurrence

Insights into systems of polynomials with real coefficients

Abstract

Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.