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A K3 surface associated to certain integral matrices with integral eigenvalues

Ronald van Luijk
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Abstract

In this article we will show that there are infinitely many symmetric, integral 3 x 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 Neron-Severi group of this surface and find all low degree curves on it.

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Ronald van Luijk. 2005-06-11. A K3 surface associated to certain integral matrices with integral eigenvalues. https://arxiv.org/abs/math/0411600

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