Arithmetic and Geometric Progressions in Productsets over Finite Fields

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dc.creatorShparlinski, Igor E.
dc.date2007-11-12
dc.date2007-11-13
dc.date.accessioned2026-07-07T08:42:23Z
dc.date.available2026-07-07T08:42:23Z
dc.descriptionGiven two sets $\cA, \cB \subseteq \F_q$ of elements of the finite field $\F_q$ of $q$ elements, we show that the productset $$ \cA\cB = \{ab | a \in \cA, b \in\cB\} $$ contains an arithmetic progression of length $k \ge 3$ provided that $k<p$, where $p$ is the characteristic of $\F_q$, and $# \cA # \cB \ge 3q^{2d-2/k}$. We also consider geometric progressions in a shifted productset $\cA\cB +h$, for $f \in \F_q$, and obtain a similar result.
dc.identifierhttps://arxiv.org/abs/0711.1800
dc.identifierhttp://arxiv.org/abs/0711.1800
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141943
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11B83, 11T23, 11T30
dc.titleArithmetic and Geometric Progressions in Productsets over Finite Fields
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