Spinor genera of unimodular 𝑍-lattices in quadratic fields

Earnest, A. G.

doi:10.1090/S0002-9939-1977-0441863-0

Spinor genera of unimodular $Z$-lattices in quadratic fields
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by A. G. Earnest

Proc. Amer. Math. Soc. 64 (1977), 189-195

DOI: https://doi.org/10.1090/S0002-9939-1977-0441863-0

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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 $L{ \otimes _{\mathbf {Z}}}\mathcal {O}$.

References

A. G. Earnest and J. S. Hsia, Spinor genera under field extensions. I, Acta Arith. 32 (1977), no. 2, 115–128. MR 434950, DOI 10.4064/aa-32-2-115-128
A. G. Earnest and J. S. Hsia, Spinor genera under field extensions. II. $2$ unramified in the bottom field, Amer. J. Math. 100 (1978), no. 3, 523–538. MR 491488, DOI 10.2307/2373836
A. G. Earnest and J. S. Hsia, Spinor genera under field extensions. II. $2$ unramified in the bottom field, Amer. J. Math. 100 (1978), no. 3, 523–538. MR 491488, DOI 10.2307/2373836
J. S. Hsia, Spinor norms of local integral rotations. I, Pacific J. Math. 57 (1975), no. 1, 199–206. MR 374029, DOI 10.2140/pjm.1975.57.199

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