On the existence of infinite, non-trivial F-sets

JOURNAL OF NUMBER THEORY

卷:168

Article

Ferraguti, Andrea¹  Micheli, Giacomo² 

[1] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[2] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

关键词: Polynomials;    Finite fields;    F-sets;   

DOI  :  10.1016/j.jnt.2016.03.024

来源: Elsevier

【 摘 要 】

In this paper we prove a conjecture of J. Andrade, S.J. Miller, K. Pratt and M. Trinh, showing the existence of a non-trivial infinite F-set over F-q[x] for every fixed q. We also provide the proof of a refinement of the conjecture, involving the notion of width of an F-set, which is a natural number encoding the complexity of the set. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free