A type of hyperelliptic continued fraction
T.G.Berry
Abstract
Based on hints of Tschebychev, a continued fraction
is described which gives an effective algorithm for
calculating the torsion, if finite, of
divisors D-D- on a hyperelliptic curve of genus
> 1, where
D is an effective divisor of
degree 2 and D- denotes the image of D under the hyperelliptic
involution. The
difficulties involved in extending the algorithm to divisors of
degree
> 2 are briefly discussed.
AMS 2000 subject classification: 14Q05, 11Y55. Keywords: hyperelliptic
curve, torsion divisor, continued fraction.
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On 16 Apr 2004, 14:01.