Maximal hyperelliptic curves of genus three
نویسندگان
چکیده
منابع مشابه
Maximal hyperelliptic curves of genus three
Article history: Received 24 June 2008 Revised 29 January 2009 Available online 27 February 2009 Communicated by H. Stichtenoth This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, ...
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The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one comes from the period map, which realizes this variety as a sub-variety of the Siegel modular variety of level two and genus three H3/Γ3[2]. We denote the hyperelliptic locus by I3[2] ...
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Let C/Q be a curve of genus three, given as a double cover of a plane conic. Such a curve is hyperelliptic over the algebraic closure of Q, but may not have a hyperelliptic model of the usual form over Q. We describe an algorithm that computes the local zeta functions of C at all odd primes of good reduction up to a prescribed bound N . The algorithm relies on an adaptation of the ‘accumulating...
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and all the coefficients belong to Z[ζ]. (These facts seem to be already known to Eisenstein [6]). Therefore the product of the roots {℘(u)} except for 0 of the numerator is equal to ±b, and the product of reciprocals of the roots {℘(u)} of the denominator is equal to b. So we have factorization of b or b in an extended integer ring of Z[ζ]. Analogous fact is known for a function ℘(u) satisfyin...
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Article history: Received 14 April 2008 Revised 6 December 2009 Communicated by Gebhard Böckle
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2009
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2009.02.002