On the Rank of Universal Quadratic Forms over Real Quadratic Fields

Abstrakt

We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field Q 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.

Klíčová slova

• Rank
• Universal
• Forms
• Real
• Quadratic
• Fields