Fourier Analysis on Number Fields (Graduate Texts in Mathematics) pdf epub mobi txt 电子书 下载 2025
- 数学
- 数论
- 代数数论7
- 代数数论
- number_theory
- Math
- 分析
- 代数
The general aim of this book is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. The more particular goal is to cover John Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries--technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tate's thesis are somewhat terse and less than complete, our intent is to be more leisurely, more comprehensive, and more comprehensible. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. While the choice of objects and methods is naturally guided by specific mathematical goals, the approch is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. Moreover, the work should be a good reference for working mathematicians interested in any of these fields. Specific topics include: topologcial groups, representation theory, duality for locally compact abelian groups, the structure of arithmetic fields, adeles and ideles, an introduction to class field theory, and Tate's thesis and applications.
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写得太啰嗦，不过取材还不错
评分写得太啰嗦，不过取材还不错
评分我…读不下去，太啰嗦了……材料选的不错
评分写得太啰嗦，不过取材还不错
评分不错。用调和分析的角度来看待代数数论。 算是GL(1)的表示论。 不过，另外一本用解析语言写代数数论的书很值得读 L.J. Goldstein, Analytic Number Theory
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