Department of Mathematics, University of Texas at Arlington
Department of Mathematics, University of North Texas
Department of Mathematics, Texas Christian University
Date/Time/Room: Wednesday (11/21/2001) at 4:00 pm in 487 Pickard Hall
(Refreshments served at 3:30 pm)
Department of Mathematics, Harvard University
and National Central University, Taiwan
``Non-Archimedean dynamics, Drinfeld modules and a
theorem of Schinzel''
Let $a$ be a nonzero element of a number field $K$. Assume that
$a$ is not a root of unity, then Schinzel's theorem on primitive
divisors said that for almost all positive integer $n$, it occurs
as the multiplicative order of $a$ modulo $\wp$ for some finite
place $\wp$ of $K$. In the setting of Drinfeld modules, we show
that an analogous phenomenon exists. Some non-archimedean
dynamics will be studied in order to prove our result.
We will also discuss generalizations of Schinzel's theorem made
by J. Silverman to the case of elliptic curves over $\mathbb Q$
and by J. Choen and S. Hahn to the case of elliptic curves over
arbitrary number fields.