R202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
On Common Divisors of Elliptic Sequences over Function Fields
Liang-Chung Hsia (
National Taiwan Normal University
)
Abstract
In this talk, we'll discuss the common divisors among sequences arising from cyclic groups generated by rational points
of elliptic curves
(
) defined over the function field
of a smooth projective curve
over
. More precisely, let
be the elliptic surfaces over
with generic fiber
and let
be sections (corresponding to points
of the generic fibers) of
(for
). The question that we're concerned with is whether or not there are infinitely many
such that for some integers
we have
on
(for
). We provide an answer to this question. A special case of our result answers a conjecture made by Silverman.
This is a joint work with Dragos Ghioca and Tom Tucker.