The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields

Details The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields

2007-10-26

arxiv.org/abs/0710.4991v2

Mathematics

Number Theory

20 Pages

Scientific paper

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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