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An elementary approach to toy models for D. H. Lehmer’s conjecture. (English. Russian original) Zbl 1293.11067

Izv. Math. 75, No. 6, 1093-1106 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 6, 3-16 (2011).
Summary: We use the theory of algebraic fields to establish that none of the shells of the lattice \( \mathbb{Z}^2\) (resp. \( A_2\)) is a 4-design (resp. 6-design). We discuss the connection between spherical designs and imaginary quadratic fields.

MSC:

11F27 Theta series; Weil representation; theta correspondences
05B30 Other designs, configurations
11F30 Fourier coefficients of automorphic forms
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