On the number of rational points on an algebraic curve over a finite field
نویسندگان
چکیده
منابع مشابه
The fluctuations in the number of points on a hyperelliptic curve over a finite field
Article history: Received 4 May 2008 Revised 26 August 2008 Available online 21 October 2008 Communicated by J. Brian Conrey The number of points on a hyperelliptic curve over a field of q elements may be expressed as q + 1 + S where S is a certain character sum. We study fluctuations of S as the curve varies over a large family of hyperelliptic curves of genus g. For fixed genus and growing q,...
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Article history: Received 14 July 2008 Revised 9 February 2009 Available online 10 March 2009 Communicated by Neal Koblitz
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In the paper [11], Sziklai posed a conjecture on the number of points of a plane curve over a finite field. Let C be a plane curve of degree d over Fq without an Fq-linear component. Then he conjectured that the number of Fq-points Nq(C) of C would be at most (d− 1)q+1. But he had overlooked the known example of a curve of degree 4 over F4 with 14 points ([10], [1]). So we must modify this conj...
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We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here, we let both q and m vary; our estimate is explicit and does not depend on the elliptic curve.
متن کاملOn the Exponents of the Group of Points of an Elliptic Curve over a Finite Field
We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here we let both q and m vary and our estimate is explicit and does not depend on the elliptic curve.
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 1998
ISSN: 1370-1444
DOI: 10.36045/bbms/1103409013