On the number of point of given order on odd degree hyperelliptic curves
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS(2022)
摘要
For integers $N\geq 3$ and $g\geq 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.
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关键词
odd degree hyperelliptic curves,hyperelliptic curves
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