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Real quadratic fields with a universal quadratic form of given rank have density zero
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We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite quadratic lattices that represent all the multiples of a given rational integer. Our main tools are short vectors in quadratic lattices combined with an estimate for the number of periodic continued fractions with bounded coefficients.
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Cited by 2 Pith papers
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Kitaoka's Conjecture for quadratic fields
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