The ring of modular forms of $\mathrm{O}(2,4;\mathbb{Z})$ with characters

Atsuhira Nagano; Kazushi Ueda

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arXiv · 2005.00231

The ring of modular forms of $\mathrm{O}(2,4;\mathbb{Z})$ with characters

Atsuhira Nagano·Kazushi Ueda

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Abstract

We show that the ring of modular forms with characters for $\mathrm{O}(2,4;\mathbb{Z})$ is generated by forms of weights 4, 4, 6, 8, 10, 10, 12, and 30 with three relations of weights 8, 20, and 60. The proof is based on the study of a moduli space of K3 surfaces.

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Atsuhira Nagano, Kazushi Ueda. 2020-05-01. The ring of modular forms of $\mathrm{O}(2,4;\mathbb{Z})$ with characters. https://arxiv.org/abs/2005.00231

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