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UNIVERSAL QUADRATIC FORMS AND ELEMENTS OF SMALL NORM IN REAL QUADRATIC FIELDS

Part of: Algebraic number theory: global fields Forms and linear algebraic groups

Published online by Cambridge University Press:  11 January 2016

VÍTĚZSLAV KALA
VÍTĚZSLAV KALA*
Affiliation:
Mathematisches Institut, Bunsenstr. 3–5, D-37073 Göttingen, Germany Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18600 Praha 8, Czech Republic email [email protected]
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Abstract

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For any positive integer $M$ we show that there are infinitely many real quadratic fields that do not admit $M$-ary universal quadratic forms (without any restriction on the parity of their cross coefficients).

Keywords

universal quadratic formreal quadratic number fieldcontinued fraction

MSC classification

Primary: 11E12: Quadratic forms over global rings and fields
Secondary: 11R11: Quadratic extensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 7 - 14
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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