In this paper we construct the first known explicit family of K3 surfaces defined over the rationals that are proved to have geometric Picard number 3. This family is dense in one of the componentsâ€¦ (More)

In this paper, we study the Markoff-Hurwitz equations x0 + ...+x 2 n = ax0 Â· Â· Â·xn. The variety V defined by this equation admits a group of automorphisms A âˆ¼= Z/2âˆ—Â· Â· Â·âˆ—Z/2 (an n+1 fold freeâ€¦ (More)

In this paper, we investigate a K3 surface with Picard number three and present evidence that strongly suggests a canonical vector height cannot exist on this surface.

In an earlier paper by the first author, an argument for the nonex-istence of canonical vector heights on K3 surfaces of Picard number three was given, based on an explicit surface that was notâ€¦ (More)

The problem of counting lattice points on a hyperboloid of two sheets is Gaussâ€™ circle problem in hyperbolic geometry. The problem of counting lattice points on a hyperboloid of one sheet does notâ€¦ (More)

In this paper, we demonstrate via an example a variety of techniques both general and ad hoc that can be used to find the group of automorphisms of a K3 surface. Introduction Given a K3 surface X/kâ€¦ (More)

We begin this number with a diierent feature. Arthur Baragar has provided us with a personal account of his experiences as Deputy L e a d e r t o the 40 th IMO in Romania. He is a professor at theâ€¦ (More)

1. INTRODUCTION. It is impossible to trisect an arbitrary angle. So mathematicians have claimed, with confidence, for more than 160 years. The statement is provocative. To a mathematician, theâ€¦ (More)