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Transactions of the American Mathematical Society

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Orbits in unimodular Hermitian lattices

Author: Donald G. James
Journal: Trans. Amer. Math. Soc. 332 (1992), 849-860
MSC: Primary 11E39; Secondary 11E08, 11H06, 20G25, 20G30
MathSciNet review: 1089419
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Abstract: Let $ L$ be a unimodular indefinite hermitian lattice over the integers $ \mathfrak{o}$ of an algebraic number field, and $ N(L,c)$ the number of primitive representations of $ c \in \mathfrak{o}$ by $ L$ that are inequalivant modulo the action of the integral special unitary group $ SU(L)$ on $ L$. The value of $ N(L,c)$ is determined from the local representations via a product formula.

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Additional Information

Keywords: Unimodular hermitian forms, algebraic integers, integral representations, unitary group, orbits, local fields, cyclotomic fields
Article copyright: © Copyright 1992 American Mathematical Society

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