منابع مشابه
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
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 ...
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Let E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ Q − {±1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over Ln in certain cases. The aim of this note is to explain how some of th...
متن کاملCurves with many points
Introduction. Let C be a (smooth, projective, absolutely irreducible) curve of genus g > 2 over a number field K. Faltings [Fa1, Fa2] proved that the set C(K) of K-rational points of C is finite, as conjectured by Mordell. The proof can even yield an effective upper bound on the size #C(K) of this set (though not, in general, a provably complete list of points); but this bound depends on the ar...
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Let n be a positive integer, and let d = (d1, d2, . . . , dn) be an n-tuple of integers such that di ≥ 2 for all i. A hypertorus Q d n is a simple graph defined on the vertex set {(v1, v2, . . . , vn) : 0 ≤ vi ≤ di − 1 for all i}, and has edges between u = (u1, u2, . . . , un) and v = (v1, v2, . . . , vn) if and only if there exists a unique i such that |ui − vi| = 1 or di − 1, and for all j ≠ ...
متن کاملPaired many-to-many disjoint path covers in faulty hypercubes
A paired many-to-many k-disjoint path cover (k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all the vertices of the graph. Extending the notion of DPC, we define a paired many-to-many bipartite k-DPC of a bipartite graph G to be a set of k disjoint paths joining k distinct source-sink pairs that altogether cover the same number of vertic...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2000
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0286