Boris Venkov's Theory of Lattices and Spherical Designs

Boris Venkov passed away on November 10 2011 just 5 days before his 77th birthday. This article gives a short survey of the mathematical work of Boris Venkov in this direction.

[1]  Helmut Koch,et al.  Über ganzzahlige unimodulare euklidische Gitter. , 1989 .

[2]  W. Ebeling,et al.  Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch , 1994 .

[3]  Noam D. Elkies.  Lattices and codes with long shadows , 1995 .

[4]  G. Nebe,et al.  Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14 , 2008, 0809.0593.

[5]  Oliver D. King,et al.  A mass formula for unimodular lattices with no roots , 2000, Math. Comput..

[6]  Wolfgang Ebeling,et al.  Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch , 1994 .

[7]  Gabriele Nebe,et al.  The strongly perfect lattices of dimension $10$ , 2000 .

[8]  S. Böcherer.  Über den Kern der Thetaliftung , 1990 .

[9]  Richard E. Borcherds,et al.  A Siegel cusp form of degree 12 and weight 12 , 1998 .

[10]  Jean-Pierre Serre.  A Course in Arithmetic , 1973 .

[11]  Gabriele Nebe,et al.  On lattices whose minimal vectors form a 6-design , 2009, Eur. J. Comb..

[12]  C. Siegel,et al.  Berechnung von Zetafunktionen an ganzzahligen Stellen , 1979 .

[13]  B. M. Fulk.  MATH , 1992 .

[14]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[15]  N. Sloane,et al.  The Shadow Theory of Modular and Unimodular Lattices , 1998, math/0207294.

[16]  Even unimodular Euclidean lattices of dimension 32.II , 1984 .

[17]  Helmut Koch,et al.  Über gerade unimodulare Gitter der Dimension 32, III , 1991 .

[18]  Akihiro Munemasa,et al.  Classification of ternary extremal self-dual codes of length 28 , 2009, Math. Comput..

[19]  J. Seidel,et al.  SPHERICAL CODES AND DESIGNS , 1991 .

[20]  J. Martinet.  Perfect Lattices in Euclidean Spaces , 2010 .

[21]  B. Venkov.  Even unimodular Euclidean lattices in dimension 32 , 1984 .

[22]  Henry Cohn,et al.  New upper bounds on sphere packings I , 2001, math/0110009.

[23]  Unimodular lattices and strongly regular graphs , 1985 .

[24]  G. Nebe,et al.  On Siegel modular forms of weigth 12 , 2001 .

[25]  Hiroyuki Yoshida.  The action of Hecke operators on theta series , 1985 .

[26]  C. Bachoc,et al.  Modular Forms, Lattices and Spherical Designs , 2000 .

[27]  Akihiro Munemasa,et al.  The nonexistence of certain tight spherical designs , 2005 .

[28]  Gabriele Nebe,et al.  Low dimensional strongly perfect lattices. I: The 12-dimensional case , 2005 .

[29]  Thomas C. Hales.  Sphere packings, I , 1997, Discret. Comput. Geom..

[30]  M. Kneser,et al.  Klassenzahlen definiter quadratischer Formen , 1957 .

[31]  Rudolf Scharlau,et al.  The genus of the Barnes-Wall lattice , 1994 .

[32]  H. Quebbemann.  Modular Lattices in Euclidean Spaces , 1995 .

[33]  Gabriele Nebe,et al.  Unimodular lattices with long shadow , 2003 .

[34]  Gabriele Nebe,et al.  On tight spherical designs , 2012, 1201.1830.