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| 一部学习数论和群论的研究生教程 |
| 《数域上傅里叶分析(英文版)》 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 |
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