Even unimodular 12-dimensional quadratic forms over \({\mathbb{Q}}(\sqrt{5})\)

DOI10.1016/0001-8708(87)90009-0zbMath0622.10015OpenAlexW2024169663MaRDI QIDQ1090698

Patrick J. Costello, J. S. Hsia

Publication date: 1987

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(87)90009-0

zbMATH Keywords

theta seriesHilbert modular formsroot systemLeech latticemass formulaSiegel's formulaintegral quadratic formseven unimodular latticesrepresentations of numbers

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Quadratic forms over global rings and fields (11E12) Holomorphic modular forms of integral weight (11F11) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (6)

Unimodular lattices over real quadratic fields ⋮ Even unimodular 8-dimensional quadratic forms over \({\mathbb{Q}}(\sqrt{2})\) ⋮ On the genera and the class number of unimodular lattices over the ring of integers in real quadratic fields ⋮ Automorphic forms for some even unimodular lattices ⋮ A Moonshine path for \(5A\) and associated lattices of ranks 8 and 16. ⋮ ON EPSTEIN'S ZETA FUNCTION OF HUMBERT FORMS

Cites Work

• Klassenzahlen definiter quadratischer Formen
• Automorphism groups of 24-dimensional even unimodular lattices
• Quaternions over \(Q(\sqrt5)\), Leech's lattice and the sporadic group of Hall-Janko
• On the classification of integral even unimodular 24-dimensional quadratic forms
• On the enumeration of lattices of determinant one
• Die Bestimmung der Funktionen zur Hilbertschen Modulgruppe des Zahlkörpers \(Q(\sqrt 5)\)
• A characterisation of Leech's lattice
• Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern
• Definite quadratische Formen der Dimension 24 und Diskriminante 1
• Theta series of quaternary quadratic forms over Z and Z[(1 + √p)/2]
• A construction of integral lattices
• The Modular Groups of Hilbert and Siegel
• Notes on Sphere Packings
• On the uniqueness of the Golay codes
• Sphere Packings and Error-Correcting Codes
• Regular positive ternary quadratic forms
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