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, Volume 120, Issue 1, pp 83–90 | Cite as

Totally positive extensions and weakly isotropic forms

  • Karim Johannes BecherEmail author


The aim of this article is to analyse a new field invariant, relevant to (formally) real fields, defined as the supremum of the dimensions of all anisotropic, weakly isotropic quadratic forms over the field. This invariant is compared with the classical u-invariant and with the Hasse number. Furthermore, in order to be able to obtain examples of fields where these invariants take certain prescribed values, totally positive field extensions are studied.

Classification (MSC 2000)

11E04 11E81 12D15 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Fachbereich Mathematik und Statistik, D203Universität KonstanzKonstanzGermany

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