A singular K3 surface related to sums of consecutive cubes
Abstract
We study the surface arising from the diophantine equation m3+(m+1)3+...+(m+k-1)3=l2. 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.
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