Jacques Martinet

• phone: +33-5-40-00-60-96 (From France : 05-56-84-60- 96)
• fax     : +33-5-56-84-69-50 (From France : 05-40-00-69-50)

martinet a` math point u-bordeaux1 DOT fr

• Université Bordeaux 1
  Institut de Mathématiques de Bordeaux (I.M.B.)
  351, cours de la Libération
  33405, Talence cedex
  France

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Mise à jour / Last update: February 9th, 2010

Links to WEB pages of some mathematicians working on lattices and/or coding theory.

Other links

Photos de la fête "septante" photos ;

Anne-Marie BERGÉ, obituary, J. Théorie Nombres Bordeaux 20, fasc. 2 (2008), i--xi :

First part and photograph pdf ; Second part dvi , postscript , pdf.

Recent publications

BOOKS
• Les réseaux parfaits des espaces euclidiens, Éditions Masson, Paris, 1996 ; maintenant : Éditions Dunod.
• Erratum au livre "Les réseaux parfaits des espaces euclidiens". dvi, postscript, pdf.
• Perfect Lattices in Euclidean Spaces, Springer-Verlag, Grundleheren der Mathematischen Wissenschaften 327, Heidelberg, 2003.
• Preface, Introduction and Contents of the book "Perfect Lattices in Euclidean Spaces". postscript. pdf.
• Corrected and extended reference list of the book "Perfect Lattices in Euclidean Spaces". dvi , postscript , pdf.
• Comparison between the French and English editions. dvi , postscript , pdf.
• Erratum to the book "Perfect Lattices in Euclidean Spaces". dvi , postscript , pdf.
• Complements to the book "Perfect Lattices in Euclidean Spaces". dvi , postscript , pdf.
• Réseaux euclidiens, designs sphériques et formes modulaires, L'Enseignement Mathématique, Monographie 37, Genève, 2001.
• Contents of the book "Réseaux euclidiens, designs sphériques et formes modulaires". dvi , postscript , pdf.
• Introduction of the book "Réseaux euclidiens, designs sphériques et formes modulaires". dvi , postscript , pdf.
• Erratum and Complements to "Réseaux euclidiens, designs sphériques et formes modulaires". dvi , postscript , pdf.
• PUBLICATION LIST.
• (Liste des publications.) dvi , postscript , pdf ; Math. Reviews .
• ARTICLES
• Histoire des Journées Arithmétiques, J. Théorie des Nombres de Bordeaux 7 (1995), vii - xiii. (Mise à jour pour les J.A. 2009 de Saint-´Etienne.) dvi , postscript , pdf.
• On Successive Minima of Rings of Algebraic Integers (extended abstract and comments). Acts of the conference ANTS III, Portland, Oregon,1998; Springer Lectures Notes in Computer Science 1423 (1998), 424 - 432. dvi , postscript , pdf.
• Perfect and Eutactic Lattices: Extensions of Voronoi's Theory, in Voronoi's impact on modern science, edited by P. Engel and H. Syta, Proc. Inst. Math. National Acad. Sc. Ukraine, vol. 21, Book 1, pp. 186 - 198. dvi , postscript , pdf .
• Algebraic Constructions of Lattices; Isodual Lattices, Acts of the 1996 Eger conference, Györy, Pethö, Sós, eds, Walter de Gruyter GmbH, Berlin-New York, 1998, pp. 349 - 360. dvi , postscript , pdf .
• Réseaux et designs sphériques, Notes d'un cours fait par Boris VENKOV d'octobre 1996 à février 1997 ; in Réseaux euclidiens, designs sphériques et formes modulaires (J. Martinet, éditeur), L'Enseignement Mathématique, Monographie nu. 37, 2001. dvi , postscript.
• Les réseaux fortement eutactiques (avec Boris VENKOV), in Réseaux euclidiens, designs sphériques et formes modulaires (J. Martinet, éditeur), L'Enseignement Mathématique, Monographie nu. 37, 2001. dvi , postscript , pdf.
• Sur certains designs sphériques liés à des réseaux entiers, in Réseaux euclidiens, designs sphériques et formes modulaires (J. Martinet, éditeur), L'Enseignement Mathématique, Monographie nu. 37, 2001. [WARNING: O23 was missing in the statement of the Theorem.] dvi , postscript , pdf .
• Sur l'indice d'un sous-réseau, in Réseaux euclidiens, designs sphériques et formes modulaires (J. Martinet, éditeur), L'Enseignement Mathématique, Monographie nu. 37, 2001. dvi , postscript.
• Reduction Modulo 2 and 3 of Euclidean Lattices, J. Algebra 251 (2002), 864-887. dvi , postscript , pdf .
• Appendix to "Reduction Modulo 2 and 3 of Euclidean Lattices": the proof, Preprint 1999, Université Bordeaux 1. dvi , postscript , pdf .
• The Perfection Default Module of a Euclidean Lattice, Talk at a congress held in Marseille-Luminy, September 2000; Preprint 2000, Université Bordeaux 1. dvi , postscript , pdf .
• L'arithmétique des algèbres de quaternions, un mini-cours de trois heures donné à Lausanne (Suisse) en Avril 2002 ; dvi , postscript , pdf .
• Compl\'ement \`a L'arithmétique des algèbres de quaternions, dvi , postscript , pdf . Link to E. Hallouin/C. Maire Christian Maire
• Symmetric Groups and Lattices (with Anne-Marie BERGÉ) Monatshefte für Mathematik 140 (2003), 179-195. dvi , postscript , pdf .
• Reduction Modulo 2 and 3 of Euclidean Lattices, II, Acts of the Talca Conference (Chile, December 2002), Contemporary Math. 344 (2004), 265-273. dvi , postscript , pdf .
• On integral lattices having an odd minimum (with Boris VENKOV) Algebra and Analysis (Saint-Petersburg) 16, 3 (2004), 99-142; =St-Petersburg Math. J. (AMS translations), 507-539. dvi , postscript , pdf .
• On Parity Classes, Preprint 2003, Université Bordeaux 1 (after lectures held in Lausanne (Suisse) in May 2003); dvi , postscript , pdf .
• A generalization of some lattices of Coxeter (with Anne-Marie BERGÉ), Mathematika 51 (2004), 49-61. dvi , postscript , pdf .
• Sublattices of certain Coxeter lattices (with Anne-Marie BERGÉ), A paper dedicated to Georges Gras, J. Th. Nombres Bordeaux 17 (2005), 455-465. dvi , postscript , pdf .
[This is a footnote to Anne-Marie Bergé's paper "On certain Coxeter lattices without perfect sections", J. Alg. Comb. 20 (2004), 5-16.]
• On weakly eutactic forms (with Anne-Marie BERGÉ), submitted December 9th, 2005; J. London Math. Soc. 75 (2007), 187-198. dvi , postscript , pdf .
• On perfection relations in lattices (with Anne-Marie BERGÉ), Contemporary Math. {\bf 493} (2009), 29--49; arXiv:math.NT/0611220 v 1 (8 Nov. 2006); click here ,
• Bases of minimal vectors in lattices, I , Archiv der Mathematik 89 (2007), 404-410. dvi , postscript , pdf .
• Bases of minimal vectors in lattices, II, Archiv der Mathematik 89 (2007),541-551 . dvi , postscript , pdf .
• On classifying Minkowskian sublattices (with Wolfgang KELLER and Achill SCHÜRMANN), updated though not in final form of the paper with the same title in [arXiv click here]; dvi , postscript , pdf .
• By Marc GINGRAUX, J. Th. Nombres Bordeaux 21 (2009), 535--557 (to appear). pdf .

A Catalogue of Perfect Lattices (Prepared jointly with Christian BATUT)

1. About perfect lattices. (The second file is a text file.)



• Perfection: An introductory paper about perfect lattices. dvi , postscript , pdf .
• Statistics in dimension 8 : Statistics on perfect 8-dimensional lattices.
• Eutactic and semi-eutactic perfect, $8$-dimensional lattices, after Cordian RIENER , "On extreme forms in dimension 8", J. Th. Nombres Bordeaux 18 (2006), 677-682. dvi , postscript , pdf .
• Numerical data for the paper above: read_me , eutax8 .



2. Tables and GP-access.

• Perfect lattices in dimensions 2 to 7 : Gram matrices after Conway and Sloane; pn[i] gives P_n^i.
• gp-access to 7-dimensional perfect LLL-reduced lattices.
• gp-access to 8-dimensional perfect Laihem lattices.
• gp-access to 8-dimensional perfect Baril lattices.
• gp-access to 8-dimensional perfect Napias lattices.
• gp-access to 8-dimensional perfect Batut lattices.



3. Tables of 8-dimensional perfect lattices in PARI-GP format.
   These tables are to be loaded, and then read by gp together with the corresponding access files.

• Table for the Laihem lattices : 1175 lattices.
• Table for the Baril lattices. : 53 lattices.
• First table for the Napias lattices : 1000 lattices.
• Second table for the Napias lattices : 1000 lattices.
• Third table for the Napias lattices : 1000 lattices.
• Fourth table for the Napias lattices : 1000 lattices.
• Fifth table for the Napias lattices : 1000 lattices.
• Sixth table for the Napias lattices : 1000 lattices.
• Seventh table for the Napias lattices : 1000 lattices.
• Eighth table for the Napias lattices : 1000 lattices.
• Ninth table for the Napias lattices : 1000 lattices.
• Tenth table for the Napias lattices :   542 lattices.
• Table for the Batut lattices : 146 lattices.



4. Tables of various (very often perfect) lattices in PARI-GP format. (Nov. 2004)
   These tables can be loaded under PARI-GP; the comments can be read with an editor.

• Some Lattices contained in the Leech lattice : Lattices Lambda_n, K_n, K'_n, Plesken-Pohst for minimum 4, ...
• Antilaminations of O_{23}.
• Plesken-Pohst lattices of minimum 3.
• Some Integral Lattices of Minimum 6.



5. Voronoi graphs in dimensions 2 to 7; minimal classes in dimensions 2 to 4. (Dec. 2004)
   The three PARI-GP files can be loaded under PARI-GP; the comments can be read with an editor (e.g., emacs).



• Voronoi graphs and minimal classes. dvi , postscript , pdf .
• The Voronoi graphs in dimensions 2 to 6.
• The Voronoi graph in dimension 7.
• Minimal classes in dimensions 2 to 4.



6. Strongly eutactic and strongly perfect lattices.
   The two PARI-GP files can be loaded under PARI-GP; the comments can be read with an editor (e.g., emacs).



• Lattices and spherical designs. dvi , postscript , pdf .
• Strongly (semi-)eutactic lattices (dimensions 2 to 6: complete; 7,8,9: examples).
• Strongly perfect lattices (dimensions 2 to 26.)



• Some lattices of Roland Bacher (Nov. 28th, 2008) after Invent. Math. 130 (1997), 153--158.

  Lattices in dimensions 28 to 22.)

  
  

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