staple
With cedram.org

Search the site

Table of contents for this issue | Previous article | Next article
Caroline Desreumaux
Construction de formes automorphes réflectives sur un espace de dimension 4
Journal de théorie des nombres de Bordeaux, 18 no. 1 (2006), p. 89-111, doi: 10.5802/jtnb.535
Article PDF | Reviews MR 2245877 | Zbl 05070449

Résumé - Abstract

Following V. Gritsenko and V. Nikulin’s works, using methods related to Jacobi forms for the root lattice $A_2,$ we can define six automorphic reflectiv forms, that will be associated to hyperbolic Kac Moody algebras of Borcherds type, for the signature $(1,3).$ For four of them a denominator formula will be given. Such a formula enables to describe the algebra totally.

Bibliography

[Bo1] R. Borcherds, Automorphic forms on $O_{s+2,2}$ and infinite products. Invent. Math. Vol. 120 (1995), 161–213.  MR 1323986 |  Zbl 0932.11028
[Bo2] R. Borcherds, Automorphic forms with singularities on Grassmanians. Invent. Math. 132 (1998), 491–562.  MR 1625724 |  Zbl 0919.11036
[B] N. Bourbaki, Groupes et algèbres de Lie. Chapitres 4, 5, 6.  Zbl 0483.22001
[D] C. Desreumaux, Formes de Jacobi relatives au réseau de racines $A_2$ et applications. Thèse numéro 3295, Université de Lille 1, juin 2003.
[EZ] M. Eichler, D. Zagier, The theory of Jacobi forms. Progress in Math. 55, Birkhaüser, Boston, Basel, Stuttgart, 1985.  MR 781735 |  Zbl 0554.10018
[G] V. Gritsenko, Modular forms and moduli spaces of abelian and $K3$ surfaces. St. Petersburg Math. J., Vol. 6 (1995), No.6, 1179–1208.  MR 1322120 |  Zbl 0847.14020
[GH] V. Gritsenko, K. Hulek, Minimal Siegel modular threefolds. Mathem. Proc. Cambridge Phil. Soc. 123 (1998), 461–485.  MR 1607981 |  Zbl 0930.11028
[GN1] V. Gritsenko, V. Nikulin, Automorphic Forms and Lorentzian Kac–Moody Algebras. Part I. Int. J. of Math., Vol. 9 (1998), No. 2, 153–199.  MR 1616925 |  Zbl 0935.11015
[GN2] V. Gritsenko, V. Nikulin, Automorphic Forms and Lorentzian Kac–Moody Algebras. Part II. Int. J. of Math., Vol. 9 (1998), No. 2, 201–275.  MR 1616929 |  Zbl 0935.11016
[GN3] V. Gritsenko, V. Nikulin, On classification of Lorentzian Kac–Moody Algebras. Russian Math. Survey, Vol. 57 (2002), 79–139.  MR 1992083 |  Zbl 1057.17018
[KP] V.G. Kac, D.H. Peterson, Infinite dimensional Lie Algebras, Theta Functions and Modular Forms. Advances in Mathematics 53 (1984), 125–264.  MR 750341 |  Zbl 0584.17007
[Mu] D. Mumford, Tata Lectures on Theta I. Progress in Mathematics, vol. 28, Birkhäuser, 1983.  MR 688651 |  Zbl 0509.14049
[W] K.Wirthmüller, Root systems and Jacobi forms. Compositio Mathematica 82 (1992), 293–354. Numdam |  MR 1163219 |  Zbl 0780.17006