Classification of integral lattices with large class number

DOI10.1090/S0025-5718-98-00938-7zbMath0919.11031OpenAlexW2053054295MaRDI QIDQ4383191

Rudolf Scharlau, Boris Hemkemeier

Publication date: 24 March 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00938-7

zbMATH Keywords

integral latticeextremal modular latticeclass number of a genusneighbour method

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to number theory (11-04) Class numbers of quadratic and Hermitian forms (11E41) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items (20)

Seven-modular lattices and a septic base Jacobi identity. ⋮ One-class genera of maximal integral quadratic forms ⋮ Applications of coding theory to the construction of modular lattices ⋮ Siegel modular forms of weight 13 and the Leech lattice ⋮ On characteristic polynomials of automorphisms of Enriques surfaces ⋮ Kneser's method of neighbors ⋮ Counting elliptic fibrations on \(\mathrm{K}3\) surfaces ⋮ Quaternary quadratic lattices over number fields ⋮ Computations of Cyclotomic Lattices ⋮ Quadratic Forms and Automorphic Forms ⋮ LOW-DIMENSIONAL STRONGLY PERFECT LATTICES. III: DUAL STRONGLY PERFECT LATTICES OF DIMENSION 14 ⋮ Automorphisms of modular lattices ⋮ Low dimensional strongly perfect lattices. IV: The dual strongly perfect lattices of dimension 16 ⋮ Reflective Lorentzian lattices of signature \((5,1)\) ⋮ The shadow theory of modular and unimodular lattices ⋮ Lattice Methods for Algebraic Modular Forms on Classical Groups ⋮ Reflection groups of Lorentzian lattices ⋮ Symplectic group lattices ⋮ Zonal functions for the unitary groups and applications to Hermitian lattices. ⋮ Borcherds' method for Enriques surfaces

Cites Work

• Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen
• Klassenzahlen definiter quadratischer Formen
• Spinor equivalence of quadratic forms
• On the classification of integral even unimodular 24-dimensional quadratic forms
• The genus of the Barnes-Wall lattice
• Computing isometries of lattices
• Modular lattices in Euclidean spaces
• Neighborhood in the sense of Kneser for quaternionic lattices
• Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern
• Definite quadratische Formen der Dimension 24 und Diskriminante 1
• Constructing integral lattices with prescribed minimum. I
• Low-dimensional lattices. IV. The mass formula
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Classification of integral lattices with large class number