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Erschienen in:

12.03.2023

On arithmetic progressions in finite fields

verfasst von: Abílio Lemos, Victor G. L. Neumann, Sávio Ribas

Erschienen in: Designs, Codes and Cryptography | Ausgabe 6/2023

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Abstract

In this paper, we explore the existence of m-term arithmetic progressions in \({\mathbb {F}}_{q^n}\) with a given common difference whose terms are all primitive elements, and at least one of them is normal. We obtain asymptotic results for \(m \ge 4\) and concrete results for \(m \in \{2,3\}\), where the complete list of exceptions when the common difference belongs to \({\mathbb {F}}_{q}\) is obtained. The proofs combine character sums, sieve estimates and computational arguments using the software SageMath.

Vorheriger Artikel Diagonal cellular factor pair Latin squares

Nächster Artikel On finite generalized quadrangles with as an automorphism group

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Titel: On arithmetic progressions in finite fields
verfasst von: Abílio Lemos
Victor G. L. Neumann
Sávio Ribas
Publikationsdatum: 12.03.2023
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 6/2023
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-023-01201-z

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On arithmetic progressions in finite fields

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