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- chapter
1 pdf last
release (31.01.2006): compilation of the first 3 lectures.
Bibliography for chapter 1
:
- A. Borel, Introduction aux
groupes arithmétiques, Hermann
Paris 1969 (in french); chapitre 1.
- J.W.S. Cassels, An Introduction to the Geometry of Numbers,
Grundlehren der Mahematischen Wissenschaften 99.
- Y. Kitaoka, Arithmetic of
quadratic forms,
Cambridge University
Press, Cambridge, 1993;
chapter 2.
- J. Martinet, Perfect Lattices in Euclidean Spaces, Springer
2003
or
J. Martinet, Les réseaux parfaits des espaces
euclidiens, Masson 1996.
- chapter 2 Lecture 4 (06.02.2006) pdf
Bibliography for chapter 2
:
- W. Ebeling, Lattices and codes, Friedr. Vieweg & Sohn,
Braunschweig,2002.
- J.E. Humphreys, Reflection groups and
Coxeter Groups,
Cambridge University
Press, Cambridge, 1990.
- J. Martinet, loc. cit.
- chapter 3 Lectures 5 and 6 (20.02.2006 &
27.02.2006) pdf
Bibliography for chapter 3
:
- W. Ebeling, Lattices and codes, Friedr. Vieweg & Sohn,
Braunschweig,2002.
- J. Martinet, loc. cit.
- chapter 4 Lectures 7, 8, 9 and 10 pdf
Bibliography for chapter 4
:
- W. Ebeling, Lattices and codes, Friedr. Vieweg & Sohn,
Braunschweig,2002.
- R. Gunnings, Lectures on Modular forms,
Princeton U.P. 1962.
- T. Miyake, Modular forms, Springer 1976.
- A. Ogg, Modular forms and Dirichlet Series,
Benjamin 1969.
- J.-P. Serre, Cours d'arithmétique,
Presses Universitaires de France 1970; last chapter.
- James
Milne's on-line lecture notes on modular forms http://www.jmilne.org/math/CourseNotes/math678.html
Caution: conventions
and
notation vary from one author to the other, especially regarding the weight of a modular
form.
- chapter 4 Lecture 11 (03.04.2006) pdf
- chapter 5 Lecture
12 (10.04.2006) pdf
- chapter 5 Lecture
13 (24.04.2006) pdf
Bibliography for chapter 5 :
- J.W.S. Cassels, An Introduction to the Geometry of Numbers,
Grundlehren der Mahematischen Wissenschaften 99.
- R. Coulangeon, Réseaux
k-extrêmes, Proc.
London Math. Soc. (3) 73 (1996),
no. 3, 555-574.
- ___________ , Voronoï
theory over algebraic number fields, Monographies de
l'Enseignement Mathématique no 37 (2001), 147-162.
- M. I. Icaza, Hermite constant and
extreme forms for algebraic number fields, J. London Math. Soc. (2) 55
(1997), no. 1, 11--22.
- M. Morishita, T. Watanabe,
Adèle geometry of numbers.
Class field theory---its
centenary and prospect (Tokyo, 1998), 509--536, Adv. Stud. Pure Math. 30, Math. Soc. Japan, Tokyo, 2001.
- J. Neukirch, Algebraic number
theory, Grundlehren der Mathematischen
Wissenschaften, 322. Springer-Verlag, Berlin, 1999.
- S. Ohno, T. Watanabe, Estimates of
Hermite constants for algebraic number fields. Comment. Math.
Univ. St. Paul. 50 (2001), no. 1, 53--63.
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