数域上的傅里叶分析
2011-7-1
无世界图书出版公司
罗摩克里希纳
350
无
《数域上傅里叶分析(英文版)》是一部学习数论和群论的研究生教程。每章的引入也是十分有意思，对历史材料的深入理解和作者对相关内容独到的理解和表达方式，使得本书组成一个有机的整体，这些正是一个初学者所需要的。同时，这本书也很适合于科研人员。书中包括了不少比较复杂的内容，使得这本书的部分内容比较难懂，也是本书吸引读者的一个原因。每章的后面都附有习题。
读者对象：数学专业的研究生，教师和相关专业的科研人员。
preface
index of notation
1 topolooical groups
1.1 basic notions
1.2 haar measure
1.3 profinite groups
1.4 pro-p-groups
exercises
2 some representation theory
2.1 representations of locally compact groups
2.2 banach algebras and the gelfand transform
2.3 the spectral theorems
2.4 unitary representations
exercises
3 duality for locally compact abelian groups
3.1 the pontryagin dual
3.2 functions of positive type
3.3 the fourier inversion formula
3.4 pontryagin duality
exercises
4 the structure of arithmetic fields
4.1 the module of an automorphism
4.2 the classification of locally compact fields
4.3 extensions of local fields
4.4 places and completions of global fields
4.5 ramification and bases
exercises
5 adeles, ideles, and the class groups
5.1 restricted direct products, characters, and measures
5.2 adeles, ideles, and the approximation theorem
5.3 the geometry of ak/k
5.4 the class groups
exercises
6 a quick tour of class field theory
6.1 frobenius elements
6.2 the tchebotarev density theorem
6.3 the transfer map
6.4 artin's reciprocity law
6.5 abelian extensions of q and qr
exercises
7 tate's thesis and applications
7.1 local -functions
7.2 the riemann-roch theorem
7.3 the global functional equation
7.4 hecke l-functions
7.5 the volume of c1k and the regulator
7.6 dirichlet's class number formula
7.7 nonvanishing on tile line re(s)=1
7.8 comparison of hecke l-functions
exercises
appendices
appendix a: normed linear spaces
a.1 finite-dimensional normed linear spaces
a.2 the weak topology
a.3 the weak-star topology
a.4 a review of lr-spaces and duality
appendix b: dedekind domains
b.1 basic properties
b.2 extensions of dedekind domains
references
index
无