Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Classification of integral lattices with
large class number


Authors: Rudolf Scharlau and Boris Hemkemeier
Journal: Math. Comp. 67 (1998), 737-749
MSC (1991): Primary 11E41; Secondary 11H55, 11--04
MathSciNet review: 1458224
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 of $\ell$-elementary lattices, for small prime level $\ell,$ are obtained. For instance, the class number of $12$-dimensional $7$-elementary even lattices of determinant $7^6$ is $395$; no extremal lattice in the sense of Quebbemann exists. The implementation incorporates as essential parts previous programs of W. Plesken and B. Souvignier.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11E41, 11H55, 11--04

Retrieve articles in all journals with MSC (1991): 11E41, 11H55, 11--04


Additional Information

Rudolf Scharlau
Affiliation: Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
Email: Rudolf.Scharlau@mathematik.uni-dortmund.de

Boris Hemkemeier
Affiliation: Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
Email: Boris.Hemkemeier@mathematik.uni-dortmund.de

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00938-7
PII: S 0025-5718(98)00938-7
Keywords: Lattice, integral quadratic form, class number of genus, neighbour method, $p$-elementary lattice, extremal modular lattice
Received by editor(s): January 11, 1995
Received by editor(s) in revised form: October 7, 1996
Article copyright: © Copyright 1998 American Mathematical Society