On the distribution of rational functions along a curve over Fp and residue races

Andrew Granville; Igor E. Shparlinski; Alexandru Zaharescu

doi:10.1016/j.jnt.2005.02.002

On the distribution of rational functions along a curve over F_p and residue races

Andrew Granville
, Igor E. Shparlinski
, Alexandru Zaharescu

Mathematics

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

Abstract

Let p be a prime number, let F̄_p be the algebraic closure of F_p = ℤ/pℤ, let C be an absolutely irreducible curve in A^r (F̄_p) and h = (h₁,...,h_s) a rational map defined on the curve C. We investigate the distribution in the s-dimensional unit cube (ℝ/ℤ)^s of the images through h of the F_p-points of C, after a suitable embedding.

Original language	English (US)
Pages (from-to)	216-237
Number of pages	22
Journal	Journal of Number Theory
Volume	112
Issue number	2
DOIs	https://doi.org/10.1016/j.jnt.2005.02.002
State	Published - Jun 2005

Keywords

Affine curves
Discrepancy
Distribution on the torus

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jnt.2005.02.002

Library availability

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Cite this

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abstract = "Let p be a prime number, let {\=F}p be the algebraic closure of Fp = ℤ/pℤ, let C be an absolutely irreducible curve in Ar ({\=F}p) and h = (h1,...,hs) a rational map defined on the curve C. We investigate the distribution in the s-dimensional unit cube (ℝ/ℤ)s of the images through h of the Fp-points of C, after a suitable embedding.",

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AU - Shparlinski, Igor E.

AU - Zaharescu, Alexandru

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AB - Let p be a prime number, let F̄p be the algebraic closure of Fp = ℤ/pℤ, let C be an absolutely irreducible curve in Ar (F̄p) and h = (h1,...,hs) a rational map defined on the curve C. We investigate the distribution in the s-dimensional unit cube (ℝ/ℤ)s of the images through h of the Fp-points of C, after a suitable embedding.

KW - Affine curves

KW - Discrepancy

KW - Distribution on the torus

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