The spinor genus of the integral trace

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.

arXiv commentThere have been some minor changes in sections 1 and 2 of the paper. Section 3 is completely new. Comments are welcome