Universal optimality of the \(E_8\) and Leech lattices and interpolation formulas

DOI10.4007/annals.2022.196.3.3OpenAlexW2913291429MaRDI QIDQ2092827

Henry Cohn, Stephen D. Miller, Abhinav Kumar, Danylo V. Radchenko, Maryna S. Viazovska

Publication date: 3 November 2022

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.05438

zbMATH Keywords

energy minimizationmodular formsFourier interpolationuniversal optimality

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Classical equilibrium statistical mechanics (general) (82B05) Holomorphic modular forms of integral weight (11F11) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Discrete potential theory (31C20)

Related Items (20)

Perturbed Fourier uniqueness and interpolation results in higher dimensions ⋮ Optimality of the triangular lattice for Lennard–Jones type lattice energies: a computer-assisted method ⋮ Fourier non-uniqueness sets from totally real number fields ⋮ A note on Schwartz functions and modular forms ⋮ Generalized sign Fourier uncertainty ⋮ Saturating unitarity bounds at U-duality symmetric points ⋮ The work of Maryna Viazovska ⋮ Asymptotics of \(k\)-nearest neighbor Riesz energies ⋮ From sphere packing to Fourier interpolation ⋮ Perturbed interpolation formulae and applications ⋮ Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture ⋮ Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies ⋮ Short Communication: Weak Sparse Superresolution is Well-Conditioned ⋮ Lattice-based cryptography: a survey ⋮ Soft Riemann‐Hilbert problems and planar orthogonal polynomials ⋮ A quantitative stability result for the sphere packing problem in dimensions 8 and 24 ⋮ The smallest interacting universe ⋮ Nonhexagonal Lattices From a Two Species Interacting System ⋮ An optimal uncertainty principle in twelve dimensions via modular forms ⋮ An extremal property of the hexagonal lattice

Uses Software

• Mathematica

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