## 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)

Zbl 0706.11018
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### References:

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