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Even Quadratic Forms with Cube-Free Discriminant

Donald G. James
Proceedings of the American Mathematical Society
Vol. 106, No. 1 (May, 1989), pp. 73-79
DOI: 10.2307/2047376
Stable URL: http://www.jstor.org/stable/2047376
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Even Quadratic Forms with Cube-Free Discriminant
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Abstract

A formula is given for the number of genera of even lattices with $\operatorname{rank} n$, signature $s$, and discriminant $(-1)^{(n - s)/2}d^2D$, when $dD$ is odd and square-free. In the indefinite case, an orthogonal splitting of these lattices into simple components is also determined.

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