SHELLS OF SELFDUAL LATTICES VIEWED AS SPHERICAL DESIGNS

DOI10.1142/S0218196705002797zbMath1084.05015arXivmath/0502313OpenAlexW1967163087MaRDI QIDQ3379486

Claude Pache

Publication date: 6 April 2006

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502313

zbMATH Keywords

modular form

Mathematics Subject Classification ID

Other designs, configurations (05B30) Lattices and convex bodies (number-theoretic aspects) (11H06) Numerical quadrature and cubature formulas (65D32) Automorphic forms, one variable (11F12)

Related Items (9)

Design-theoretic analogies between codes, lattices, and vertex operator algebras ⋮ A note on Assmus-Mattson type theorems ⋮ Construction of spherical cubature formulas using lattices ⋮ SPHERICAL DESIGNS FROM THE NORM-3 SHELL OF INTEGRAL LATTICES ⋮ Spherical designs and modular forms of the \(D_4\) lattice ⋮ A dimensionally continued Poisson summation formula ⋮ On the existence of extremal Type II ℤ_{2𝕜}-codes ⋮ Toy models for D. H. Lehmer's conjecture ⋮ A survey on spherical designs and algebraic combinatorics on spheres

Cites Work

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• Irreducibility of unitary group representations and reproducing kernels Hilbert spaces. Appendix on two point homogeneous compact ultrametric spaces in collaboration with Rostislav Grigorchuk.
• Spherical designs and finite group representations (some results of E. Bannai).
• A characterization of the \(\mathbb Z^ n\) lattice
• Lattices and codes with long shadows
• Sur la lacunarité des puissances de η
• The strongly perfect lattices of dimension 10

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