Abstract
Abstract
Let
be an algebraically closed field of characteristic different from
,
a positive integer,
a polynomial of degree
with coefficients in
and without multiple roots,
the corresponding hyperelliptic curve of genus
over
, and
its Jacobian. We identify
with the image of its canonical embedding in
(the infinite point of
goes to the identity element of
). It is well known that for every
there are exactly
elements
such that
. Stoll constructed an algorithm that provides the Mumford representations of all such
in terms of the Mumford representation of
. The aim of this paper is to give explicit formulae for the Mumford representations of all such
in terms of the coordinates
, where
is given by a point
. We also prove that if
1$?>
, then
does not contain torsion points of orders between
and
.
Cited by
7 articles.
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