ar X iv : m at h / 99 09 03 7 v 1 [ m at h . A G ] 6 S ep 1 99 9 Kummer Covers with Many Points
نویسنده
چکیده
Let p be a prime and Fq be a finite field with q = p m elements and let F̄q be an algebraic closure of Fq . In this paper we present a method for constructing curves over finite fields with many points which are Kummer covers of P, or of other suitable base curves. For this we look at rational functions f ∈ Fq(x) such that f assumes a fixed value a ∈ Fq on a (preferably large) set P ⊆ P(Fq). To take a concrete example we set a = 1. Then the algebraic curve which is the Kummer covering of P given by the equation
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ar X iv : h ep - e x / 99 10 03 6 v 1 1 8 O ct 1 99 9 EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN – EP / 99 – 139 7 October 1999
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تاریخ انتشار 1999