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TNT 2012-2013
Instructors: Philippe Michel & Nahid Walji
Course notes weeks 15-20 (à venir)
Pour l'examen les notes de cours s'arretent à la fin de la section 4 du Chapître 3 p.45
Exercises
Week 1: Background on Dirichlet characters and the gamma function.
Weeks 2-5: The functional equation for Dirichlet L-functions: PDF1 PDF2.
Week 6: Gauss sums. PDF
Weeks 7-10: Harmonic homogeneous polynomials PDF1 PDF2 PDF3
Week 11-12: Theta functions PDF1 PDF2
A beautiful movie by Doug Arnold and Jon Rognes
Références:
Bump, Daniel Automorphic forms and representations. Cambridge Studies in Advanced Mathematics, 55. Cambridge University Press, Cambridge, 1997.
Faraut Jacques Analyse sur les groupes de Lie, Une introduction, Mathématiques en devenir, calvage et Mounet, Paris 2006.
Goldfeld, Dorian Automorphic forms and $L$-functions for the group ${\rm GL}(n,\bold R)$. With an appendix by Kevin A. Broughan. Cambridge Studies in Advanced Mathematics, 99. Cambridge University Press, Cambridge, 2006.
Iwaniec, Henryk Topics in classical automorphic forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997.
Serre, Jean-Pierre Cours d'arithmétique. Le Mathématicien, No. 2. Presses Universitaires de France, Paris, 1977.