A K3 Surface Associated With Certain Integral Matrices Having Integral Eigenvalues

Abstract

AbstractIn this article we will show that there are infinitely many symmetric, integral 3× 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by proving that the rational points on a certain non-Kummer, singular K3 surface are dense. We will also compute the entire Néron–Severi group of this surface and find all low degree curves on it.