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The length and other invariants of a real field

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Abstract

The length of a field is the smallest integer m such that any totally positive quadratic form of dimension m represents all sums of squares. We investigate this field invariant and compare it to others such as the u-invariant, the Pythagoras number, the Hasse number, and the Mordell function related to sums of squares of linear forms.

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Authors and Affiliations

  1. Zukunftskolleg / Fachbereich Mathematik und Statistik, Fach D216, Universität Konstanz, 78457, Konstanz, Germany

    Karim Johannes Becher

  2. Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA

    David B. Leep

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  1. Karim Johannes Becher
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  2. David B. Leep
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Correspondence to Karim Johannes Becher.

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Becher, K.J., Leep, D.B. The length and other invariants of a real field. Math. Z. 269, 235–252 (2011). https://doi.org/10.1007/s00209-010-0724-3

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  • DOI: https://doi.org/10.1007/s00209-010-0724-3

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