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Quick asymptotic upper bounds for lattice kissing numbers

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

Nils-Peter Skoruppa
Nils-Peter Skoruppa
Affiliation:
Fachbereich Mathematik. Universität Siegen, Walter-Flex-Straβe 3, 57068 Siegen, Germany. E-mail:skoruppa@math.uni-siegen.de
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Abstract

General upper bounds for lattice kissing numbers are derived using Hurwitz zeta functions and new inequalities for Mellin transforms.

MSC classification

Secondary: 11H31: Lattice packing and covering
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 51 - 57
Copyright
Copyright © University College London 2002

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References

[C–S]Conway, J. H. and Sloane, N. J. A.. Sphere Packings, Lattices and Groups (Springer Verlag. 1988).CrossRefGoogle Scholar
[F–S]Friedman, E. and Skoruppa, N.-P.. Lower Bounds for the Lp-norm in terms of the Mellin transform. Bull. London Math. Soc., 25 (1993), 567–572.CrossRefGoogle Scholar
[K–L]Kabatiansky, G. A. and Levenshtein, V. I.. Bounds for packings on a sphere and in space. Problems of Information Transmission 14 (1978) 1–17.Google Scholar
[S]Skoruppa, N.-P.. Quick lower bounds for regulators of number fields. Enseign. Math. 39 (1993), 137–141.Google Scholar
[S–W]Stein, E. and Weiss, G.. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press 1971).Google Scholar
[W]Wyner, A. D.. Capabilities of bounded discrepancy decoding. AT&T Technical Journal, 44 (1965), 1061–1122.Google Scholar
[Z]Zong, C., Sphere Packings (Springer Verlag 1999).Google Scholar