The spinor genus of the integral trace. (English) Zbl 1410.11031
Summary: 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.
MSC:
| 11E12 | Quadratic forms over global rings and fields |
| 11R04 | Algebraic numbers; rings of algebraic integers |
| 11S99 | Algebraic number theory: local fields |
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