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

DOI10.1017/S0004972715001495zbMath1345.11025arXiv1507.04237OpenAlexW2259969192WikidataQ111976476 ScholiaQ111976476MaRDI QIDQ3186372

Vítězslav Kala

Publication date: 9 August 2016

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.04237

zbMATH Keywords

continued fractionreal quadratic number fielduniversal quadratic form

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic forms over global rings and fields (11E12)

Related Items (17)

Norms of indecomposable integers in real quadratic fields ⋮ Sums of squares in rings of integers with 2 inverted ⋮ A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number field ⋮ On Kitaoka's conjecture and lifting problem for universal quadratic forms ⋮ Lifting problem for universal quadratic forms over totally real cubic number fields ⋮ Trace and norm of indecomposable integers in cubic orders ⋮ The sum of four squares over real quadratic number fields ⋮ Lifting problem for universal quadratic forms ⋮ Universal quadratic forms over multiquadratic fields ⋮ On the rank of universal quadratic forms over real quadratic fields ⋮ Sums of squares in \(S\)-integers ⋮ There are no universal ternary quadratic forms over biquadratic fields ⋮ Indecomposable integers in real quadratic fields ⋮ Composition of binary quadratic forms over number fields ⋮ Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields ⋮ Additive structure of totally positive quadratic integers ⋮ Number fields without universal quadratic forms of small rank exist in most degrees

Cites Work

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• Quaternary universal forms over \(\mathbb Q(\sqrt{13})\)
• Universal octonary diagonal forms over some real quadratic fields.
• Quadratic Forms Representing All Odd Positive Integers
• On continued fractions of given period
• Number fields without n-ary universal quadratic forms
• Universality of a non-classical integral quadratic form over Q ( \sqrt 5 )

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