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

By Vítězslav Kala. Bulletin of the Australian Mathematical Society, 2015

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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).

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/258aafbf51d43dcf6a8231bacfe5a8d0688027e2