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arXiv · 2512.22520

The $L$-function of the surface parametrizing cuboids

Madoka Horie·Takuya Yamauchi
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Abstract

In this note, we compute the $L$-function of the projective smooth surface $S$ over $\mathbb{Q}$ that parametrizes cuboids whose geometric properties are studied in detail by Stoll and Testa. As a byproduct, we completely determine the structure of ${\rm Pic}(S_{\overline{\mathbb{Q}}})$ as a ${\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$-module.

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Madoka Horie, Takuya Yamauchi. 2025-12-27. The $L$-function of the surface parametrizing cuboids. https://arxiv.org/abs/2512.22520

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