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2022 Evaluation of polynomials over finite rings via additive combinatorics
Gyula Károlyi, Csaba Szabó
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Publ. Mat. 66(1): 197-205 (2022). DOI: 10.5565/PUBLMAT6612208

Abstract

We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics, which may be of independent interest.

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Gyula Károlyi. Csaba Szabó. "Evaluation of polynomials over finite rings via additive combinatorics." Publ. Mat. 66 (1) 197 - 205, 2022. https://doi.org/10.5565/PUBLMAT6612208

Information

Received: 14 April 2020; Accepted: 4 September 2020; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612208

Subjects:
Primary: 16Z05
Secondary: 11B75 , 13M10 , 16P10

Keywords: additive combinatorics , Chevalley’s theorem , dichotomy , equation solvability problem , nilpotent rings , Olson’s theorem , polynomial method

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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