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)

Speaker: Liang-Chung Hsia, Department of Mathematics, Harvard University
                  and National Central University, Taiwan

``Non-Archimedean dynamics, Drinfeld modules and a theorem of Schinzel''

Abstract: 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.