JournalsdmVol. 23pp. 15–34

On the Rank of Universal Quadratic Forms over Real Quadratic Fields

  • Valentin Blomer

    University of Göttingen, Mathematisches Institut, Bunsenstr. 3-5, D-37073 Göttingen, Germany

  • Vítězslav Kala

    University of Göttingen, Mathematisches Institut, Bunsenstr. 3-5, D-37073 Göttingen, Germany and Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 83, 18600 Praha 8, Czech Republic
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Abstract

We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field and obtain lower and upper bounds for it in terms of certain sums of coefficients of the associated continued fraction. We also estimate such sums in terms of and establish a link between continued fraction expansions and special values of -functions in the spirit of Kronecker's limit formula.

Cite this article

Valentin Blomer, Vítězslav Kala, On the Rank of Universal Quadratic Forms over Real Quadratic Fields. Doc. Math. 23 (2018), pp. 15–34

DOI 10.4171/DM/611