Unimodular lattices with long shadow Original Research Article

Let L be an odd unimodular lattice of dimension n with shadow n−16. If min(L)greater-or-equal, slanted3 then dim(L)less-than-or-equals, slant46 and there is a unique such lattice in dimension 46 and no lattices in dimensions 44 and 45. To prove this, a shadow theory for theta series with spherical coefficients is developed.