Experimental Mathematics

Computations of cyclotomic lattices

Christian Batut, Heinz-Georg Quebbemann, and Rudolf Scharlau

Abstract

We study even modular lattices having level $\ell$ and dimension $2(p-\nobreak 1)$, for p prime, and arising from the ideal class group of the p-th cyclotomic extension of $\Q(\sqrt{-\ell})$. After giving the basic theory we concentrate on Galois-invariant ideals, obtain computational results on minimal vectors and isometries, and identify several old or new extremal lattices.

Article information

Source
Experiment. Math., Volume 4, Issue 3 (1995), 177-179.

Dates
First available in Project Euclid: 3 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1062621076

Mathematical Reviews number (MathSciNet)
MR1387475

Zentralblatt MATH identifier
0873.11026

Subjects
Primary: 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07]

Keywords
lattice integral quadratic form Craig lattice hermitian lattice modular lattice extremal lattice isodual Hermite number cyclotomic ideal

Citation

Batut, Christian; Quebbemann, Heinz-Georg; Scharlau, Rudolf. Computations of cyclotomic lattices. Experiment. Math. 4 (1995), no. 3, 177--179. https://projecteuclid.org/euclid.em/1062621076


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