Universal positive quaternary quadratic lattices over totally real number fields

DOI10.1112/S0025579300012651zbMath0895.11017OpenAlexW2114794570MaRDI QIDQ4384735

Azar N. Khosravani, Andrew G. Earnest

Publication date: 20 September 1998

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0025579300012651

zbMATH Keywords

quadratic latticequaternary quadratic formtotally real number field

Mathematics Subject Classification ID

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Quadratic forms over global rings and fields (11E12)

Related Items (15)

On primitively 2-universal quadratic forms ⋮ The universal quaternary quadratic form with the maximal discriminant ⋮ Positive definite binary Hermitian forms with finitely many exceptions ⋮ Strictly regular quaternary quadratic forms and lattices ⋮ 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 ⋮ Lifting problem for universal quadratic forms ⋮ Universal quadratic forms over multiquadratic fields ⋮ Universal binary positive definite Hermitian lattices ⋮ There are no universal ternary quadratic forms over biquadratic fields ⋮ Composition of binary quadratic forms over number fields ⋮ A cubic ring of integers with the smallest Pythagoras number ⋮ On indefinite and potentially universal quadratic forms over number fields ⋮ Number fields without universal quadratic forms of small rank exist in most degrees

Cites Work

• Darstellung durch definite ternaere quadratische Formen
• Über die Darstellung total positiver Zahlen des Körpers \(R(\sqrt 5)\) als Summe von drei Quadraten. (On the representation od totally positive numbers of the field \(R(\sqrt 5)\) as a sum of three squares)
• The Representation of Binary Quadratic Forms by Positive Definite Quaternary Quadratic Forms
• Determination of all classes of positive quaternary quadratic forms which represent all (positive) integers
• On a Problem of Ramanujan

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