A mass formula for unimodular lattices with no roots-Reference-Cited by-同舟云学术

A mass formula for unimodular lattices with no roots

Published:2002-06-25 Issue:242 Volume:72 Page:839-863
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

King Oliver

Abstract

We derive a mass formula for n n -dimensional unimodular lattices having any prescribed root system. We use Katsurada’s formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n ≤ 30 n\leq 30 . In particular, we find the mass of even unimodular 32-dimensional lattices with no roots, and the mass of odd unimodular lattices with no roots in dimension n ≤ 30 n\leq 30 , verifying Bacher and Venkov’s enumerations in dimensions 27 and 28. We also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2003-72-242/S0025-5718-02-01455-2/S0025-5718-02-01455-2.pdf

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4. R. E. Borcherds, The Leech lattice and other lattices, Ph.D. Dissertation, University of Cambridge, 1984. Available at arXiv:math.NT/9911195 Much of this material also appears in [5].

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