# The Shadow Theory of Modular and Unimodular Lattices

@article{Rains1998TheST,
title={The Shadow Theory of Modular and Unimodular Lattices},
author={Eric M. Rains and N. J. A. Sloane},
journal={Journal of Number Theory},
year={1998},
volume={73},
pages={359-389}
}
• Published 1 December 1998
• Mathematics
• Journal of Number Theory
Abstract It is shown that an n -dimensional unimodular lattice has minimal norm at most 2[ n /24]+2, unless n =23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the bound for even unimodular lattices to strongly N -modular even lattices for N in{1, 2, 3, 5, 6, 7, 11, 14, 15, 23}, (*)and analogous bounds are established here for odd lattices satisfying certain technical conditions (which are trivial for N =1 and…

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