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The L-series of a cubic fourfold

Klaus Hulek·Remke Kloosterman
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Abstract

We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface $S$, defined over a number field K such that S^[2](K) is not empty, then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss a concrete example.

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Klaus Hulek, Remke Kloosterman. 2006-02-02. The L-series of a cubic fourfold. https://arxiv.org/abs/math/0601207

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