Geodesic
An elementary approach to toy models for D.~H.~Lehmer's conjecture
Izvestiya. Mathematics , Tome 75 (2011) no. 6, pp. 1093-1106

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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.
Keywords: theta functions, spherical $t$-designs, lattices. 
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     title = {An elementary approach to toy models for {D.~H.~Lehmer's} conjecture},
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E. Bannai; Ts. Miezaki; V. A. Yudin. An elementary approach to toy models for D.~H.~Lehmer's conjecture. Izvestiya. Mathematics , Tome 75 (2011) no. 6, pp. 1093-1106. http://geodesic.mathdoc.fr/item/IM2_2011_75_6_a0/