Computations of cyclotomic lattices

by Christian Batut and Heinz-Georg Quebbemann and Rudolf Scharlau

Abstract:
We study even modular lattices of level $\ell$ and dimension $2(p-1)$, $p$ prime, which arise 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.

Key words and phrases: lattice, integral quadratic form, Craig lattice, hermitian lattice, modular lattice, extremal lattice, isodual Hermite number, cyclotomic ideal.

1991 Mathematics Subject Classification: Primary 11E12; Secondary 11H55, 11R18, 11-04.

Published in: Experiment. Math. 4 (1995), no. 3, 177--179.

Contact: Rudolf.Scharlau@Mathematik.Uni-Dortmund.DE