Bannai, Eiichi; Miezaki, Tsuyoshi; Yudin, Vladimir A. 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. Cited in 4 Documents MSC: 11F27 Theta series; Weil representation; theta correspondences 05B30 Other designs, configurations 11F30 Fourier coefficients of automorphic forms Keywords:theta functions; spherical \( t\)-designs; lattices PDFBibTeX XMLCite \textit{E. Bannai} et al., Izv. Math. 75, No. 6, 1093--1106 (2011; Zbl 1293.11067); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 6, 3--16 (2011) Full Text: DOI arXiv