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arXiv · 0710.4991

The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields

Byeong Moon Kim·Ji Young Kim·Poo-Sung Park
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Abstract

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over $\mathbb{Q}(\sqrt{-m})$ for all m. For each imaginary quadratic field $\mathbb{Q}(\sqrt{-m})$, we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13.

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Byeong Moon Kim, Ji Young Kim, Poo-Sung Park. 2008-12-24. The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields. https://arxiv.org/abs/0710.4991

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