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Mathematics of Computation

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Even positive definite unimodular quadratic forms over $ {\bf Q}(\sqrt 3)$

Author: David C. Hung
Journal: Math. Comp. 57 (1991), 351-368
MSC: Primary 11E12; Secondary 11E41
MathSciNet review: 1079022
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Abstract: A complete list of even unimodular lattices over $ \mathbb{Q}(\sqrt 3 )$ is given for each dimension $ n = 2,4,6,8$. Siegel's mass formula is used to verify the completeness of the list. Alternate checks are given using theta series and the adjacency graph of the genus at the dyadic prime $ 1 + \sqrt 3 $.

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Keywords: Root system, Minkowski-Siegel mass, Hilbert modular form, Eisenstein series, adjacenct lattices
Article copyright: © Copyright 1991 American Mathematical Society