Strongly modular lattices with long shadow
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.

@article{JTNB_2004__16_1_187_0,
     author = {Gabriele Nebe},
     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},
     mrnumber = {2145580},
     zbl = {1078.11047},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2004__16_1_187_0/}
}
Gabriele Nebe. 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. https://jtnb.centre-mersenne.org/item/JTNB_2004__16_1_187_0/

[1] N.D. Elkies, A characterization of the n lattice. Math. Res. Lett. 2 no. 3 (1995), 321–326. | MR 1338791 | Zbl 0855.11032

[2] N.D. Elkies, Lattices and codes with long shadows. Math. Res. Lett. 2 no. 5 (1995), 643–651. | MR 1359968 | Zbl 0854.11021

[3] M. Gaulter, Lattices without short characteristic vectors. Math. Res. Lett. 5 no. 3 (1998), 353–362. | MR 1637828 | Zbl 0930.11045

[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 376536 | Zbl 0311.94002

[5] T. Miyake, Modular Forms. Springer (1989). | MR 1021004 | Zbl 05012868

[6] G. Nebe, N.J.A. Sloane, A database of lattices.

[7] H.-G. Quebbemann, Modular lattices in euclidean spaces. J. Number Th. 54 (1995), 190–202. | MR 1354045 | Zbl 0874.11038

[8] H.-G. Quebbemann, Atkin-Lehner eigenforms and strongly modular lattices. L’Ens. Math. 43 (1997), 55–65. | MR 1460122 | Zbl 0898.11014

[9] E.M. Rains, N.J.A. Sloane, The shadow theory of modular and unimodular lattices. J. Number Th. 73 (1998), 359–389. | MR 1657980 | Zbl 0917.11026