Construction of spherical cubature formulas using lattices

DOI10.1090/S1061-0022-07-00946-6zbMath1122.65028arXivmath/0505510OpenAlexW1572283717MaRDI QIDQ5297973

Claude Pache, Pierre De la Harpe, Boris B. Venkov

Publication date: 16 July 2007

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505510

zbMATH Keywords

spheremodular formmodular latticecubature formula

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Multidimensional problems (41A63) Holomorphic modular forms of integral weight (11F11) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (8)

Remarks on Hilbert identities, isometric embeddings, and invariant cubature ⋮ Orbits of the hyperoctahedral group as Euclidean designs ⋮ Spherical designs and modular forms of the \(D_4\) lattice ⋮ New asymptotic estimates for spherical designs ⋮ On positive cubature rules on the simplex and isometric embeddings ⋮ Cubature formulas in numerical analysis and Euclidean tight designs ⋮ Toy models for D. H. Lehmer's conjecture ⋮ A survey on spherical designs and algebraic combinatorics on spheres

Cites Work

• Averaging sets: A generalization of mean values and spherical designs
• Spherical codes and designs
• Tight spherical designs. I
• Expressing \((a^ 2+b^ 2+c^ 2+d^ 2)^ 3\) as a sum of 23 sixth powers
• Spherical designs and finite group representations (some results of E. Bannai).
• A minimal design of order 11 on the 3-sphere
• Improvement of the Delsarte bound for \(\tau\)-designs when it is not the best bound possible
• Modular lattices in Euclidean spaces
• McLaren's improved snub cube and other new spherical designs in three dimensions
• The vanishing of Ramanujan's function \(\tau(n)\)
• SHELLS OF SELFDUAL LATTICES VIEWED AS SPHERICAL DESIGNS
• Numerical Cubature Using Error-Correcting Codes
• Numerical Cubature from Archimedes' Hat-box Theorem
• Tight Spherical Disigns, II
• Lower bounds for spherical designs
• The nonexistence of certain tight spherical designs
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