# Finding Rational Periodic Points on Wehler K3 Surfaces

### From NZJM

**New Zealand Journal of Mathematics**

**Vol.** 39, (2009), **Pages** 133-141

**Benjamin Hutz**

Department of Mathematics and Computer Science

Amherst College

Amherst, MA

**Abstract** This article examines dynamical systems on a class of K3 surfaces in with an infinite automorphism group. In particular, this article develops an algorithm to find -rational periodic points using information modulo *p* for various primes *p*. The algorithm is applied to exhibit K3 surfaces with -rational periodic points of primitive period . A portion of the algorithm is then used to determine the Riemann zeta function modulo 3 of a particular K3 surface and find a family of K3 surfaces with Picard number two.

**Keywords** periodic points, K3 surfaces, dynamical systems.

**Classification** (MSC2000) Primary: 11G99, 14G99. Secondary: 37F99.