Strongly modular lattices with long shadow

Gabriele Nebe[1]

  • [1] Abteilung Reine Mathematik Universität Ulm 89069 Ulm, Germany

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 1, page 187-196
  • ISSN: 1246-7405

Abstract

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This article classifies the strongly modular lattices with longest and second longest possible shadow.

How to cite

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Nebe, Gabriele. "Strongly modular lattices with long shadow." Journal de Théorie des Nombres de Bordeaux 16.1 (2004): 187-196. <http://eudml.org/doc/249251>.

@article{Nebe2004,
abstract = {This article classifies the strongly modular lattices with longest and second longest possible shadow.},
affiliation = {Abteilung Reine Mathematik Universität Ulm 89069 Ulm, Germany},
author = {Nebe, Gabriele},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {strongly modular lattice; shadow of a lattice},
language = {eng},
number = {1},
pages = {187-196},
publisher = {Université Bordeaux 1},
title = {Strongly modular lattices with long shadow},
url = {http://eudml.org/doc/249251},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Nebe, Gabriele
TI - Strongly modular lattices with long shadow
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 1
SP - 187
EP - 196
AB - This article classifies the strongly modular lattices with longest and second longest possible shadow.
LA - eng
KW - strongly modular lattice; shadow of a lattice
UR - http://eudml.org/doc/249251
ER -

References

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  1. N.D. Elkies, A characterization of the ℤ n lattice. Math. Res. Lett. 2 no. 3 (1995), 321–326. Zbl0855.11032MR1338791
  2. N.D. Elkies, Lattices and codes with long shadows. Math. Res. Lett. 2 no. 5 (1995), 643–651. Zbl0854.11021MR1359968
  3. M. Gaulter, Lattices without short characteristic vectors. Math. Res. Lett. 5 no. 3 (1998), 353–362. Zbl0930.11045MR1637828
  4. C. L. Mallows, A. M. Odlysko, N. J. A. Sloane, Upper bounds for modular forms, lattices and codes. J. Alg. 36 (1975), 68–76. Zbl0311.94002MR376536
  5. T. Miyake, Modular Forms. Springer (1989). Zbl1159.11014MR1021004
  6. G. Nebe, N.J.A. Sloane, A database of lattices. http://www.research.att.com/~njas/lattices 
  7. H.-G. Quebbemann, Modular lattices in euclidean spaces. J. Number Th. 54 (1995), 190–202. Zbl0874.11038MR1354045
  8. H.-G. Quebbemann, Atkin-Lehner eigenforms and strongly modular lattices. L’Ens. Math. 43 (1997), 55–65. Zbl0898.11014MR1460122
  9. E.M. Rains, N.J.A. Sloane, The shadow theory of modular and unimodular lattices. J. Number Th. 73 (1998), 359–389. Zbl0917.11026MR1657980

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