Speaker: Professor Liang-Chung Hsia (National Central University)
Title: On zeta functions associated to $p$-adic dynamics
Time: 2010-09-30 (Thu.)  15:00 - 16:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)

The study of $p$-adic dynamics has been very active in the past ten years as a branch of arithmetic dynamics. In the study of dynamical systems, the set of periodic points play an important role. Artin and Mazur introduced a one variable function, now called the dynamical zeta function, to enumerate periodic points of the dynamical systems in question. The dynamical zeta function provide important invariant about the dynamical systems.

For $p$-adic dynamics, we consider the associated zeta functions of the dynamical systems over a non-archimedian field (in particular, a $p$-adic field). In particular, we will be mostly focusing on those dynamical systems whose zeta functions are rational functions. In the talk, we will discuss some related questions in $p$-adic dynamics and possibly some applications.
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