Computing -series of geometrically hyperelliptic curves of genus three
2016 ◽
Vol 19
(A)
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pp. 220-234
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Keyword(s):
Let$C/\mathbf{Q}$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$\mathbf{Q}$, but may not have a hyperelliptic model of the usual form over$\mathbf{Q}$. 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 remainder tree’ to matrices with entries in a quadratic field. We report on an implementation and compare its performance to previous algorithms for the ordinary hyperelliptic case.
2018 ◽
Vol 30
(1)
◽
pp. 331-354
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2004 ◽
Vol 56
(4)
◽
pp. 673-698
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Keyword(s):
2015 ◽
Vol 160
(1)
◽
pp. 167-189
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Keyword(s):
2011 ◽
Vol 363
(01)
◽
pp. 281-281
◽
1990 ◽
Vol s3-60
(1)
◽
pp. 37-67
◽
2011 ◽
Vol 3
(4)
◽
pp. 344-358
◽