E. Bannai, Ts. Miezaki, V. A. Yudin, “An elementary approach to toy models for D. H. Lehmer's conjecture”, Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 6,Pages <nobr>3

This article is cited in 5 papers

An elementary approach to toy models for D. H. Lehmer's conjecture

E. Bannai^a, Ts. Miezaki^b, V. A. Yudin^c

^a Department of Mathematics, Shanghai Jiao Tong University, China
^b Department of Mathematics, Oita National College of Technology, Japan
^c Moscow Power Engineering Institute (Technical University)

Abstract: 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.

UDC: 515.5

MSC: 05B30, 11F11, 11F30

Received: 23.03.2010

DOI: 10.4213/im4556