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N. N. Andreev, An extremal property of the icosahedron , East J. Approx. 2
1996
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N. N. Andreev, Location of points on a sphere with minimal energy , Proc. Steklov Inst. Math. 219
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O. Goldreich, S. Goldwasser, and S. Halevi, Public-key cryptosystems from lattice reduction problems , in Advances in Cryptology – CRYPTO ’97 , Lecture Notes in Computer Science, volume 1294, pp. 112–131, Springer-Verlag, Berlin, 1997
1997
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A. V. Kolushov and V. A. Yudin, Extremal dispositions of points on the sphere , Anal. Math. 23
1997
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M. Ajtai, The shortest vector problem in L 2 L_{2} is NP-hard for randomized reductions , in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing , pp. 10–19, Association for Computing Machinery, New York, 1998
1998
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2008
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J. Elstrodt, F. Grunewald, and J. Mennicke, Groups acting on hyperbolic space: harmonic analysis and number theory , Springer-Verlag, Berlin, 1998
1998
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J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups , third edition, Grundlehren der Mathematischen Wissenschaften 290
1999
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P. Nguyen, Cryptanalysis of the Goldreich-Goldwasser-Halevi cryptosystem from Crypto ’97 , in Advances in Cryptology – CRYPTO ’99 , Lecture Notes in Computer Science, volume 1666, pp. 288–304, Springer-Verlag, Berlin, 1999
1999
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T. C. Hales, Cannonballs and honeycombs , Notices Amer. Math. Soc. 47
2000
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H. Löwen, Fun with hard spheres , in K. R. Mecke and D. Stoyan, eds., Statistical physics and spatial statistics: the art of analyzing and modeling spatial structures and pattern formation , Lecture Notes in Physics 554
2000
Cited alongside, same era.
S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory , second edition, Graduate Texts in Mathematics 137
2001
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H. Cohn, New upper bounds on sphere packings II , Geom. Topol. 6
2002
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H. Cohn and A. Kumar, Algorithmic design of self-assembling structures , Proc. Natl. Acad. Sci. USA 106
2009
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H. Cohn, Order and disorder in energy minimization , Proceedings of the International Congress of Mathematicians, Hyderabad, August 19–27, 2010, Volume IV, pages 2416–2443, Hindustan Book Agency, New Delhi, 2010
2010
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Y. Kallus, V. Elser, and S. Gravel, Method for dense packing discovery , Phys. Rev. E 82
2010
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P. Q. Nguyen and B. Vallée, eds., The LLL algorithm: survey and applications , Springer-Verlag, Berlin, 2010
2010
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G. Minton, unpublished notes, 2011
2011
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S. Vance, Improved sphere packing lower bounds from Hurwitz lattices , Adv. Math. 227
2011
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H. Cohn and J. Woo, Three-point bounds for energy minimization , J. Amer. Math. Soc. 25
2012
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W. Ebeling, Lattices and codes: a course partially based on lectures by Friedrich Hirzebruch , third edition, Advanced Lectures in Mathematics, Springer Spektrum, Wiesbaden, 2013
2013
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Y. Kallus, Statistical mechanics of the lattice sphere packing problem , Phys. Rev. E 87
2013
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É. Marcotte and S. Torquato, Efficient linear programming algorithm to generate the densest lattice sphere packings , Phys. Rev. E 87
2013
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R. E. Schwartz, The five-electron case of Thomson’s problem , Exp. Math. 22
2013
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A. Venkatesh, A note on sphere packings in high dimension , Int. Math. Res. Not. 2013
2013
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A. V. Bondarenko, D. P. Hardin, and E. B. Saff, Mesh ratios for best-packing and limits of minimal energy configurations , Acta Math. Hungar. 142
2014
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H. Cohn and Y. Zhao, Energy-minimizing error-correcting codes , IEEE Trans. Inform. Theory 60
2014
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D. de Laat, F. M. de Oliveira Filho, and F. Vallentin, Upper bounds for packings of spheres of several radii , Forum Math. Sigma 2
2014
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2015
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D. de Laat and F. Vallentin, A semidefinite programming hierarchy for packing problems in discrete geometry , Math. Program. 151
2015
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C. Peikert, A decade of lattice cryptography , Cryptology ePrint Archive, Report 2015/939, https://eprint.iacr.org/2015/939
2015
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2015
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2016
Closest in time.
M. S. Viazovska, The sphere packing problem in dimensions 8 8
2016
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