An analogue of Ruzsa's conjecture for polynomials over finite fields

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Bell, Jason P.¹  Nguyen, Khoa D.² 

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

关键词: Ruzsa's conjecture;    Polynomials over finite fields;    The Polynomial Method;   

DOI  :  10.1016/j.jcta.2020.105337

来源: Elsevier

【 摘 要 】

In 1971, Ruzsa conjectured that if f : N -> Z with f(n + k) = f(n) mod k for every n, k. Nand f(n) equivalent to O(theta(n)) with theta < e then f is a polynomial. In this paper, we investigate the analogous problem for the ring of polynomials over a finite field using the Polynomial Method in combinatorics. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free