Classification of integral lattices with large class number

Autor:	Boris Hemkemeier, Rudolf Scharlau
Rok vydání:	1998
Předmět:	Modular lattice Large class Discrete mathematics Pure mathematics Algebra and Number Theory Computer program Applied Mathematics MathematicsofComputing_GENERAL Algebraic number field Computational Mathematics Quadratic equation Number theory Lattice (order) Real number Mathematics
Zdroj:	Mathematics of Computation. 67:737-749
ISSN:	1088-6842 0025-5718
DOI:	10.1090/s0025-5718-98-00938-7
Popis:	A detailed exposition of Kneser’s neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program which automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera ofℓ\ell-elementary lattices, for small prime levelℓ,\ell ,are obtained. For instance, the class number of1212-dimensional77-elementary even lattices of determinant767^6is395395; no extremal lattice in the sense of Quebbemann exists. The implementation incorporates as essential parts previous programs of W. Plesken and B. Souvignier.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c8a9b6c5c291a71ff2841feed60f4296 https://doi.org/10.1090/s0025-5718-98-00938-7 Zobrazit plný text záznamu