Pith. sign in

REVIEW 1 cited by

A mass formula for unimodular lattices with no roots

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0012231 v3 pith:OFYSX3JB submitted 2000-12-22 math.NT

classification math.NT
keywords latticesunimodularmassdimensionalevenformularootroots
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tensor Product CFTs and One-Character Extensions

    hep-th 2024-12 conditional novelty 6.0 of 10

    One-character extension characters of tensor products of small CFTs organize into compact S-invariant polynomial bases, yielding closed forms up to central charge 128 and conjectured new one-character CFTs.

Pith tools