Finding Rational Periodic Points on Wehler K3 Surfaces

Abstract

This article examines dynamical systems on a class of K3 surfaces in ${\mathbb{P}}^2\times {\mathbb{P}}^2$ with an infinite automorphism group. In particular, this article develops an algorithm to find $\mathbb{Q}$-rational periodic points using information modulo $p$ for various primes $p$. The algorithm is applied to exhibit K3 surfaces with $\mathbb{Q}$-rational periodic points of primitive period $1,...,16$. 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.

to appear New Zealand Journal of Mathematics

References in corpus (2)

• Questions on self maps of algebraic varieties
• The Hyperdeterminant and Triangulations of the 4-Cube