The sphere packing problem in dimension 24
Reads0
Chats0
TLDR
In this article, it was shown that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing.Abstract:
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.read more
Citations
More filters
Journal ArticleDOI
Optimal and non-optimal lattices for non-completely monotone interaction potentials
Laurent Bétermin,Mircea Petrache +1 more
TL;DR: In this article, the authors investigated the minimization of the energy per point of d-dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric function.
Peer Review
Snowmass White Paper: The Analytic Conformal Bootstrap
TL;DR: The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles as mentioned in this paper .
Journal ArticleDOI
Fourier optimization and prime gaps
TL;DR: In this paper, the authors investigated extremal problems in Fourier analysis and their connection to a problem in prime number theory, and improved the current bounds for the largest possible gap between consecutive primes assuming the Riemann hypothesis.
Posted Content
Errata and Addenda to Mathematical Constants
TL;DR: In this paper, the authors offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constant II (2019), both published by Cambridge University Press (CUP).
Posted Content
Upper bounds for $s$-distance sets and equiangular lines
Alexey Glazyrin,Wei-Hsuan Yu +1 more
TL;DR: In this article, it was shown that the maximum size of a spherical two-dimensional equiangular set with scalar products is at most 2π(n(n+1) 2π 2πε 2 3 n a^2 ).
References
More filters
Journal ArticleDOI
Handbook of Mathematical Functions with Formulas
TL;DR: The Handbook of Mathematical Functions with Formulas (HOFF-formulas) as mentioned in this paper is the most widely used handbook for mathematical functions with formulas, which includes the following:
Book
Tata Lectures on Theta I
TL;DR: In this paper, theta functions in one variable and motivation: motivation and theta function in several variables are compared. But the results are limited to one variable, and motivation is not considered.
Posted Content
Sphere packings I
TL;DR: A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
Journal ArticleDOI
Spherical codes and designs
TL;DR: In this paper, the authors provided an overview of spherical codes and designs, and derived bounds for the cardinality of spherical A-codes in terms of the Gegenbauer coefficients of polynomials compatible with A.
BookDOI
The Selberg trace formula for PSL (2, IR)
TL;DR: The selberg trace formula (version A) as mentioned in this paper is a trace formula for the Poincare series and the spectral decomposition of L2(? \H,?).