The spinor genus of the integral trace

Mantilla-Soler, Guillermo

doi:10.1090/tran/6723

The spinor genus of the integral trace
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Trans. Amer. Math. Soc. 369 (2017), 1611-1626 Request permission

Abstract:

Let $K$ be a number field of degree at least $3$. In this article we show that the genus of the integral trace form of $K$ contains only one spinor genus. Additionally we show that exactly $43\%$ (resp. $29\%$, resp. $58\%$) of quadratic (resp. real quadratic, resp. imaginary quadratic) fields have the same property.

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