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Configurations of rank-\(40r\) extremal even unimodular lattices \((r=1,2,3)\). (English) Zbl 1185.11044

It is shown that any extremal even unimodular lattice \(L\) of rank \(40r\) with \(r=1,2,3\) is generated by its vectors of square length \(4r\) and \(4r+2\). The authors extend M. Ozeki’s method who proved the result for \(r=1\) using theta series with harmonic coefficients [Rocky Mt. J. Math. 19, No. 3, 847–862 (1989; Zbl 0706.11018)].

MSC:

11H55 Quadratic forms (reduction theory, extreme forms, etc.)
11F11 Holomorphic modular forms of integral weight
05B30 Other designs, configurations
11H06 Lattices and convex bodies (number-theoretic aspects)

Citations:

Zbl 0706.11018
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References:

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