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

E. Bannai; T. Miezaki; V. A. Yudin

doi:10.1070/IM2011v075n06ABEH002565

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

E. Bannai^*, T. Miezaki, V. A. Yudin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We use the theory of algebraic fields to establish that none of the shells of the lattice Z² (resp. A₂) is a 4-design (resp. 6-design). We discuss the connection between spherical designs and imaginary quadratic fields.

Original language	English
Pages (from-to)	1093-1106
Number of pages	14
Journal	Izvestiya Mathematics
Volume	75
Issue number	6
DOIs	https://doi.org/10.1070/IM2011v075n06ABEH002565
Publication status	Published - 2011
Externally published	Yes

Keywords

Lattices
Spherical t-designs
Theta functions

ASJC Scopus subject areas

Mathematics(all)

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10.1070/IM2011v075n06ABEH002565

Cite this

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title = "An elementary approach to toy models for D. H. Lehmer's conjecture",

abstract = "We use the theory of algebraic fields to establish that none of the shells of the lattice Z2 (resp. A2) is a 4-design (resp. 6-design). We discuss the connection between spherical designs and imaginary quadratic fields.",

keywords = "Lattices, Spherical t-designs, Theta functions",

author = "E. Bannai and T. Miezaki and Yudin, {V. A.}",

year = "2011",

doi = "10.1070/IM2011v075n06ABEH002565",

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AU - Bannai, E.

AU - Miezaki, T.

AU - Yudin, V. A.

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Y1 - 2011

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AB - We use the theory of algebraic fields to establish that none of the shells of the lattice Z2 (resp. A2) is a 4-design (resp. 6-design). We discuss the connection between spherical designs and imaginary quadratic fields.

KW - Lattices

KW - Spherical t-designs

KW - Theta functions

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DO - 10.1070/IM2011v075n06ABEH002565

M3 - Article

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VL - 75

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EP - 1106

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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