A note on polynomial sequences modulo integers

2018/06/29 by Mohammad Javaheri, Javaheri, Mohammad
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.11359

openalex publication_date 2018/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the uniform distribution of the polynomial sequence λ(P)=(\lfloor P(k) \rfloor )_{k≥ 1} modulo integers, where P(x) is a polynomial with real coefficients. In the nonlinear case, we show that λ(P) is uniformly distributed in ℤ if and only if P(x) has at least one irrational coefficient other than the constant term. In the case of even degree, we prove a stronger result: λ(P) intersects every congruence class modulo every integer if and only if P(x) has at least one irrational coefficient other than the constant term.

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