A singular K3 surface related to sums of consecutive cubes

Masato Kuwata; Jaap Top

A singular K3 surface related to sums of consecutive cubes

Number Theory 2007-05-23 v1

Authors: Masato Kuwata , Jaap Top

Abstract

We study the surface arising from the diophantine equation $m^3+(m+1)^3+...+(m+k-1)^3=l^2$ . It turns out that this is a $K3$ surface with Picard number 20. We stduy its aritmetic properties in detail. We construct elliptic fibrations on it, and we find a parametric solution to the original equation. Also, we determine the Hasse-Weil zeta function of the surface over $Q$ .

Keywords

algebraic surfaces del pezzo surfaces surface theory

Cite

@article{arxiv.math/9910191,
  title  = {A singular K3 surface related to sums of consecutive cubes},
  author = {Masato Kuwata and Jaap Top},
  journal= {arXiv preprint arXiv:math/9910191},
  year   = {2007}
}

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