Visible Points on Curves over Finite Fields

dc.contributor.author	Shparlinski IE
dc.contributor.author	Voloch JF
dc.date.accessioned	2017-05-12T04:37:48Z
dc.date.available	2017-05-12T04:37:48Z
dc.date.issued	2013	en
dc.date.updated	2017-05-09T20:33:54Z
dc.description.abstract	For a prime 𝑝 and an absolutely irreducible modulo 𝑝 polynomial 𝑓(U,V) ∈ ℤ[U,V] we obtain an asymptotic formulas for the number of solutions to the congruence 𝑓(𝑥,𝑦) ≡ a (mod 𝑝) in positive integers 𝑥 ⩽ X, 𝑦 ⩽ Y, with the additional condition 𝗀cd(𝑥,𝑦)=1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average over 𝑎 for a fixed prime 𝑝, and also on average over 𝑝 for a fixed integer 𝑎.	en
dc.identifier.citation	Shparlinski IE, Voloch JF Visible Points on Curves over Finite Fields.	en
dc.identifier.uri	http://hdl.handle.net/10092/13455
dc.language.iso	en
dc.relation.uri	http://arxiv.org/abs/0704.2446v1	en
dc.subject	math.NT	en
dc.subject	11N69	en
dc.subject	11D79	en
dc.subject.anzsrc	Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theory	en
dc.title	Visible Points on Curves over Finite Fields	en
dc.type	Reports	en

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