Pointless hyperelliptic curves

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2013Embargo end date: 01 Jan 2012 English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 21, pages 50-57 (issn: 1071-5797,

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Authors: Ryan Becker; Darren B. Glass;

doi: 10.1016/j.ffa.2013.01.008 , 10.48550/arxiv.1209.2984

arXiv: 1209.2984

Pointless hyperelliptic curves

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Abstract

In this paper we consider the question of whether there exists a hyperelliptic curve of genus $g$ which is defined over $\FF_q$ but has no rational points over $\FF_q$ for various pairs $(g,q)$.

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Gettysburg College
United States

Keywords

Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Algebraic Geometry (math.AG)

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