Odd unimodular lattices of minimum 4. (English) Zbl 0998.11034

J. H. Conway and N. J. A. Sloane [J. Number Theory 72, 357-362 (1998; Zbl 0917.11027)] have determined the largest minimum of an \(n\)-dimensional odd unimodular lattice up through \(n=33\). In particular they show that no minimum 4 lattice exists in dimension 33. This result is extended here to dimensions 34 and 35. In the proof the shadow of a lattice and theta series with spherical coefficients are used.


11H06 Lattices and convex bodies (number-theoretic aspects)
11H50 Minima of forms


Zbl 0917.11027
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