Number Theory

Geometry of Numbers

11Hxx

  1. Kanat Abdukhalikov, Unimodular Hermitian lattices, Mathematisches Forschungsinstitut Oberwolfach Report No. 1/2005 (2005), 27–30.
  2. Kanat Abdukhalikov and Rudolf Scharlau, Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers, Math. Comp. 78 (2009), no. 265, 387–403.[MR]
  3. Christine Bachoc and Gabriele Nebe, Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order, Experiment. Math. 6 (1997), no. 2, 151–162.[MR]
  4. Christine Bachoc and Boris Venkov, Modular forms, lattices and spherical designs, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., vol. 37, Enseignement Math., Geneva, 2001, pp. 87–111.[MR]
  5. Werner Backes and Susanne Wetzel, Heuristics on lattice basis reduction in practice, ACM J. Exp. Algorithmics 7 (2002), 21 pp. (electronic).[MR]
  6. Siegfried Boecherer and Gabriele Nebe, On theta series attached to maximal lattices and their adjoints, preprint (2009), 16 pages.[arXiv]
  7. Robin Chapman, Steven T. Dougherty, Philippe Gaborit, and Patrick Solé, 2-modular lattices from ternary codes, J. Théor. Nombres Bordeaux 14 (2002), no. 1, 73–85.[MR]
  8. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1999, pp. lxxiv+703.[MR]
  9. R. Coulangeon, M. I. Icaza, and M. O'Ryan, Lenstra's constant and extreme forms in number fields, Experiment. Math. 16 (2007), no. 4, 455–462.[MR/link]
  10. Mathieu Dutour Sikirić, Achill Schürmann, and Frank Vallentin, A generalization of Voronoi's reduction theory and its application, Duke Math. J. 142 (2008), no. 1, 127–164.[MR/arXiv]
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  12. Philippe Gaborit, Construction of new extremal unimodular lattices, European J. Combin. 25 (2004), no. 4, 549–564.[MR]
  13. Paul E. Gunnells and Dan Yasaki, Perfect forms over totally real number fields, preprint (2009), 11 pages.[arXiv]
  14. Masaaki Harada, On the existence of frames of the Niemeier lattices and self-dual codes over Fp, J. Algebra 321 (2009), no. 8, 2345–2352.[MR/doi]
  15. Masaaki Harada, Masaaki Kitazume, and Michio Ozeki, Ternary code construction of unimodular lattices and self-dual codes over Z6, J. Algebraic Combin. 16 (2002), no. 2, 209–223.[MR]
  16. Boris Hemkemeier, Algorithmische konstruktionen von gittern, preprint (2004), 64 pages.[arXiv]
  17. Jacques Martinet and Achill Schürmann, On classifying Minkowskian sublattices, preprint (2009), 29 pages.[arXiv]
  18. G. Nebe, Kneser-Hecke-operators in coding theory, Abh. Math. Sem. Univ. Hamburg 76 (2006), 79–90.[MR]
  19. Gabriele Nebe, Finite quaternionic matrix groups, Represent. Theory 2 (1998), 106–223 (electronic).[MR]
  20. Gabriele Nebe, Even lattices with covering radius < √2, Beiträge Algebra Geom. 44 (2003), no. 1, 229–234.[MR]
  21. Gabriele Nebe, Strongly modular lattices with long shadow, J. Théor. Nombres Bordeaux 16 (2004), no. 1, 187–196.[MR]
  22. Gabriele Nebe, An even unimodular 72-dimensional lattice of minimum 8, preprint (2010).[arXiv]
  23. Gabriele Nebe and Kristina Schindelar, S-extremal strongly modular lattices, J. Théor. Nombres Bordeaux 19 (2007), no. 3, 683–701.[MR]
  24. Gabriele Nebe and Boris Venkov, The strongly perfect lattices of dimension 10, J. Théor. Nombres Bordeaux 12 (2000), no. 2, 503–518.[MR]
  25. Gabriele Nebe and Boris Venkov, Low-dimensional strongly perfect lattices I: The 12-dimensional case, Enseign. Math. (2) 51 (2005), no. 1-2, 129–163.[MR]
  26. Gabriele Nebe and Boris Venkov, Low dimensional strongly perfect lattices III: Dual strongly perfect lattices of dimension 14, IJNT 2 (2010), no. 2, 387–409.[arXiv]
  27. Gabriele Nebe and Chaoping Xing, A Gilbert-Varshamov type bound for Euclidean packings, Math. Comp. 77 (2008), no. 264, 2339–2344.[MR]
  28. Phong Q. Nguyen and Damien Stehlé, LLL on the average, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 238–256.[MR]
  29. W. Plesken and M. Pohst, Constructing integral lattices with prescribed minimum. I, Math. Comp. 45 (1985), no. 171, 209–221, S5–S16.[MR]
  30. W. Plesken and M. Pohst, Constructing integral lattices with prescribed minimum. II, Math. Comp. 60 (1993), no. 202, 817–825.[MR]
  31. E. M. Rains and N. J. A. Sloane, The shadow theory of modular and unimodular lattices, J. Number Theory 73 (1998), no. 2, 359–389.[MR]
  32. Achill Schürmann, Enumerating perfect forms, Proceedings of the International Conference on Quadratic Forms, Chile 2007, Contemporary Mathematics, vol. To appear, 2009, 22 pages.[arXiv]
  33. Achill Schürmann, Perfect, strongly eutactic lattices are periodic extreme, Adv. Math 225 (2010), no. 5, 2546–2564.
  34. Achill Schürmann and Frank Vallentin, Local covering optimality of lattices: Leech lattice versus root lattice E8, Int. Math. Res. Not. (2005), no. 32, 1937–1955.[MR/arXiv]
  35. Mathieu Dutour Sikirić, Achill Schürmann, and Frank Vallentin, Classification of eight-dimensional perfect forms, Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 21–32 (electronic).[MR]
  36. N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, Minimal-energy clusters of hard spheres, Discrete Comput. Geom. 14 (1995), no. 3, 237–259.[MR]
  37. Anthony Várilly-Alvarado and David Zywina, Arithmetic E8 lattices with maximal Galois action, LMS J. Comput. Math. 12 (2009), 144–165.[MR/arXiv]