The additive index of polynomials over finite fields

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2022Embargo end date: 01 May 2021 English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 79, page 102,002 (issn: 1071-5797,

Copyright policy )Funded by:NSERC | unidentified

Authors: Lucas Reis; Qiang Wang 0012;

doi: 10.1016/j.ffa.2022.102002 , 10.48550/arxiv.2105.02374

arXiv: 2105.02374

The additive index of polynomials over finite fields

- Summary
- Subjects
- Metrics

Abstract

In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds on multiplicative character sums, and characterizations of permutation polynomials.

Related Organizations

Universidade Federal de Minas Gerais
Brazil
Carleton University
Canada

Keywords

index, Mathematics - Number Theory, 11T06, 12E20, value sets, permutation polynomials, character sums, Polynomials over finite fields, linearized polynomials, FOS: Mathematics, Finite fields (field-theoretic aspects), Number Theory (math.NT), finite fields

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	2
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average