Lehmer points and visible points on affine varieties over finite fields

Kit Ho Mak; Alexandru Zaharescu

doi:10.1017/S0305004113000613

Lehmer points and visible points on affine varieties over finite fields

Kit Ho Mak
, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let V be an absolutely irreducible affine variety over 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.

Original language	English (US)
Pages (from-to)	193-207
Number of pages	15
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	156
Issue number	2
DOIs	https://doi.org/10.1017/S0305004113000613
State	Published - Mar 2014

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General Mathematics

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10.1017/S0305004113000613

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title = "Lehmer points and visible points on affine varieties over finite fields",

abstract = "Let V be an absolutely irreducible affine variety over Fp. 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.",

author = "Mak, \{Kit Ho\} and Alexandru Zaharescu",

note = "Supported by NSF grant number DMS - 0901621.",

year = "2014",

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doi = "10.1017/S0305004113000613",

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volume = "156",

pages = "193--207",

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issn = "0305-0041",

publisher = "Cambridge University Press",

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AU - Mak, Kit Ho

AU - Zaharescu, Alexandru

N1 - Supported by NSF grant number DMS - 0901621.

PY - 2014/3

Y1 - 2014/3

N2 - Let V be an absolutely irreducible affine variety over Fp. 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.

AB - Let V be an absolutely irreducible affine variety over Fp. 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.

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UR - https://www.scopus.com/pages/publications/84897585651#tab=citedBy

U2 - 10.1017/S0305004113000613

DO - 10.1017/S0305004113000613

M3 - Article

AN - SCOPUS:84897585651

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SP - 193

EP - 207

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -

Lehmer points and visible points on affine varieties over finite fields

Abstract

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