Strongly modular lattices with long shadow
Nebe, Gabriele1
1 Abteilung Reine Mathematik Universität Ulm 89069 Ulm, Germany
Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 187-196.

Cet article donne une classification des réseaux fortement modulaires dont la longueur de l’ombre prend les deux plus grandes valeurs possibles.

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

DOI : 10.5802/jtnb.441
Nebe, Gabriele 1

1 Abteilung Reine Mathematik Universität Ulm 89069 Ulm, Germany 
@article{JTNB_2004__16_1_187_0,
     author = {Nebe, Gabriele},
     title = {Strongly modular lattices with long shadow},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {187--196},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {1},
     year = {2004},
     doi = {10.5802/jtnb.441},
     zbl = {1078.11047},
     mrnumber = {2145580},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jtnb.441/}
}
TY  - JOUR
AU  - Nebe, Gabriele
TI  - Strongly modular lattices with long shadow
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2004
SP  - 187
EP  - 196
VL  - 16
IS  - 1
PB  - Université Bordeaux 1
UR  - http://archive.numdam.org/articles/10.5802/jtnb.441/
DO  - 10.5802/jtnb.441
LA  - en
ID  - JTNB_2004__16_1_187_0
ER  - 
%0 Journal Article
%A Nebe, Gabriele
%T Strongly modular lattices with long shadow
%J Journal de théorie des nombres de Bordeaux
%D 2004
%P 187-196
%V 16
%N 1
%I Université Bordeaux 1
%U http://archive.numdam.org/articles/10.5802/jtnb.441/
%R 10.5802/jtnb.441
%G en
%F JTNB_2004__16_1_187_0
Nebe, Gabriele. Strongly modular lattices with long shadow. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 187-196. doi : 10.5802/jtnb.441. http://archive.numdam.org/articles/10.5802/jtnb.441/

[1] N.D. Elkies, A characterization of the ℤ n lattice. Math. Res. Lett. 2 no. 3 (1995), 321–326. | MR | Zbl

[2] N.D. Elkies, Lattices and codes with long shadows. Math. Res. Lett. 2 no. 5 (1995), 643–651. | MR | Zbl

[3] M. Gaulter, Lattices without short characteristic vectors. Math. Res. Lett. 5 no. 3 (1998), 353–362. | MR | Zbl

[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. | MR | Zbl

[5] T. Miyake, Modular Forms. Springer (1989). | MR | Zbl

[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. | MR | Zbl

[8] H.-G. Quebbemann, Atkin-Lehner eigenforms and strongly modular lattices. L’Ens. Math. 43 (1997), 55–65. | MR | Zbl

[9] E.M. Rains, N.J.A. Sloane, The shadow theory of modular and unimodular lattices. J. Number Th. 73 (1998), 359–389. | MR | Zbl

Cité par Sources :