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Lehmer points and visible points on affine varieties over finite fields

Published online by Cambridge University Press:  14 November 2013

KIT-HO MAK  and
ALEXANDRU ZAHARESCU
KIT-HO MAK
Affiliation:
School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332, U.S.A. e-mail: [email protected]
ALEXANDRU ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801, U.S.A. e-mail: [email protected]
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Abstract

Let V be an absolutely irreducible affine variety over $\mathbb{F}_p$. A Lehmer point on V is a point whose coordinates satisfy some prescribed congruence conditions, and a visible point is one whose coordinates are relatively prime. Asymptotic results for the number of Lehmer points and visible points on V are obtained, and the distribution of visible points into different congruence classes is investigated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 193 - 207
Copyright
Copyright © Cambridge Philosophical Society 2013 

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