A mass formula for unimodular lattices with no roots

Details A mass formula for unimodular lattices with no roots A mass formula for unimodular lattices with no roots

2000-12-22

arxiv.org/abs/math/0012231v3

Mathematics of Computation, vol. 72, no. 242 (2003), 839-863.

Mathematics

Number Theory

Expanded, and some typos fixed. LaTex (27 pages) with separate ASCII table

Scientific paper

We derive a mass formula for 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 < 31. 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 < 31, 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. The ASCII text file table.txt (1.3 MB) at arXiv:math.NT/0012231 includes the complete table of masses of 32-dimensional even unimodular lattices with any given root system, and may be dowloaded using the source link.

Affiliated with

Also associated with

No associations

Rating

A mass formula for unimodular lattices with no roots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A mass formula for unimodular lattices with no roots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A mass formula for unimodular lattices with no roots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-614350