Volume 6, issue 1 (2002)

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New upper bounds on sphere packings II

Henry Cohn

Geometry & Topology 6 (2002) 329–353
Bibliography
1 G E Andrews, R Askey, R Roy, Special functions, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press (1999) MR1688958
2 R Ben Ghanem, C Frappier, Explicit quadrature formulae for entire functions of exponential type, J. Approx. Theory 92 (1998) 267 MR1604935
3 N G de Bruijn, Asymptotic methods in analysis, Dover Publications (1981) MR671583
4 H Cohn, N Elkies, New upper bounds on sphere packings I, Ann. of Math. $(2)$ 157 (2003) 689 MR1973059
5 J H Conway, N A Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften 290, Springer (1999) MR1662447
6 P J Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London (1963) MR0157156
7 A Erdélyi, W Magnus, F Oberhettinger, F G Tricomi, Higher transcendental functions Vol III, McGraw-Hill Book Company, New York-Toronto-London (1955) MR0066496
8 D V Gorbachev, An extremal problem for entire functions of exponential spherical type, which is connected with the Levenshteĭn bound for the density of a packing of $\mathbb{R}^n$ by balls, Izv. Tul. Gos. Univ. Ser. Mat. Mekh. Inform. 6 (2000) 71 MR2018751
9 L Hörmander, The analysis of linear partial differential operators I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (1990) MR1065993
10 N N Lebedev, Special functions and their applications, Dover Publications (1972) MR0350075
11 N Levinson, On a Problem of Polya, Amer. J. Math. 58 (1936) 791 MR1507202
12 E L Poiani, Mean Cesàro summability of Laguerre and Hermite series, Trans. Amer. Math. Soc. 173 (1972) 1 MR0310537
13 W Rudin, Principles of mathematical analysis, McGraw-Hill Book Co. (1976) MR0385023
14 L Schwartz, Théorie des distributions, Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann (1966) MR0209834
15 V M Sidel’nikov, Extremal polynomials used in bounds of code volume, Problems Inform. Transmission 16 (1980) 174 MR624027
16 K Stempak, Almost everywhere summability of Laguerre series, Studia Math. 100 (1991) 129 MR1121712
17 M H Stone, The generalized Weierstrass approximation theorem, Math. Mag. 21 (1948) 167, 237 MR0027121
18 G Szegö, Über gewisse Potenzreihen mit lauter positiven Koeffizienten, Math. Z. 37 (1933) 674 MR1545428
19 G Szegő, Orthogonal polynomials, American Mathematical Society (1975) MR0372517
20 S Thangavelu, Lectures on Hermite and Laguerre expansions, Mathematical Notes 42, Princeton University Press (1993) MR1215939
21 G N Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press (1944) MR0010746
22 D V Widder, The Laplace Transform, Princeton Mathematical Series 6, Princeton University Press (1941) MR0005923
23 D V Widder, Advanced calculus, Dover Books on Advanced Mathematics, Dover Publications (1989) MR1033270