Some properties of optimal functions for sphere packing in dimensions 8 and 24

H. Cohn and Y. Zhao, Energy-minimizing error-correcting codes , IEEE Trans. Inform. Theory 60

Original

1913

Earlier work this paper cites.

H. F. Blichfeldt, The minimum values of positive quadratic forms in six, seven and eight variables

1935

Earlier work this paper cites.

L. Fejes Tóth, Über einen geometrischen Satz

1940

Earlier work this paper cites.

N. N. Lebedev, Special Functions and Their Applications

1972

Earlier work this paper cites.

F. H. Stillinger, Phase transitions in the Gaussian core system

1976

Earlier work this paper cites.

V. I. Levenshtein, On bounds for packings in n n -dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245

1979

Earlier work this paper cites.

A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n n dimensions

1979

Earlier work this paper cites.

J. F. Epperson, On the Runge example

1987

Earlier work this paper cites.

G. Andrews, R. Askey, and R. Roy, Special Functions

1999

Earlier work this paper cites.

J. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups

1999

Cited alongside, same era.

P. Deift, T. Kriecherbauer, K. T-R McLaughlin, S. Venakides, and X. Zhou, Strong asymptotics of orthogonal polynomials with respect to exponential weights

1999

Cited alongside, same era.

N. Elkies, Lattices, linear codes, and invariants I

2000

Cited alongside, same era.

E. H. Lieb and M. Loss, Analysis

2001

Cited alongside, same era.

H. Cohn, New upper bounds on sphere packings II

2002

Cited alongside, same era.

H. Cohn and Y. Zhao, Sphere packing bounds via spherical codes , Duke Math. J. 163

Original

2002

Cited alongside, same era.

T. Hales, A proof of the Kepler conjecture

2005

Later among the works it cites.

H. Cohn and A. Kumar, Universally optimal distribution of points on spheres

2007

Later among the works it cites.

H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices

2009

Later among the works it cites.

H. Cohn, A. Kumar, and A. Schürmann, Ground states and formal duality relations in the Gaussian core model , Phys. Rev. E (3) 80

Original

2009

Later among the works it cites.

H. Cohn, Order and disorder in energy minimization

Original

2010

Later among the works it cites.

PARI/GP, version 2.3.5, Bordeaux, 2010, http://pari.math.u-bordeaux.fr/