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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spinor genera of unimodular $ Z$-lattices in quadratic fields


Author: A. G. Earnest
Journal: Proc. Amer. Math. Soc. 64 (1977), 189-195
MSC: Primary 10C05
DOI: https://doi.org/10.1090/S0002-9939-1977-0441863-0
MathSciNet review: 0441863
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Abstract: Let L be a unimodular Z-lattice on a quadratic space V over Q, $ \dim V \geqslant 3$, and let $ \mathcal{O}$ be the ring of algebraic integers of the quadratic field $ E = {\mathbf{Q}}(\sqrt m )$. We explicitly calculate the number of proper spinor genera in the genus of the lattice $ L{ \otimes _{\mathbf{Z}}}\mathcal{O}$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0441863-0
Keywords: Integral quadratic forms, spinor genus, quadratic lattices, quadratic extensions
Article copyright: © Copyright 1977 American Mathematical Society