The spinor genus of the integral trace

Guillermo Mantilla-Soler

The spinor genus of the integral trace

Number Theory 2015-02-19 v2

Authors: Guillermo Mantilla-Soler

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.

Keywords

spinor genus integral trace form number field quadratic fields genus theory arithmetic of quadratic forms

Cite

@article{arxiv.1306.3998,
  title  = {The spinor genus of the integral trace},
  author = {Guillermo Mantilla-Soler},
  journal= {arXiv preprint arXiv:1306.3998},
  year   = {2015}
}

Comments

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

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