P进数,P进分析和ζ函数

出版时间：2009-6  出版社：世界图书出版公司  作者：科比利兹  
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内容概要

在数论，表示理论等许多现代数学研究领域中，p进分析占据着非常重要的地位。本书是p进分析的入门教材。主要分两部分内容，首先论述p进分析理论的基本思想，其次介绍p进理论的两个重要应用，即在黎曼ζ函数值为负整数时的p进内插和在一个有限域内方程组的δ函数有理性的证明。可供数学系数论专业的研究生和研究人员参考。

书籍目录

Chapter Ⅰ　p-adic numbers　1. Basic concepts　2. Metrics on the rational numbers　　Exercises　3. Review of building up the complex numbers　4. The field of p-adic numbers　5. Arithmetic in Qp　　ExercisesChapter Ⅱ　p-adic interpolation of the Riemann zeta-function　1. A formula for .(2k)　2. p-adic interpolation of the functionf(s) = as　　Exercises　3. p-adic distributions　　Exercises　4. Bernoulli distributions　5. Measures and integration　　Exercises　6. The p-adic -function as a Mellin-Mazur transform　7. A brief survey (no proofs)  　ExercisesChapter Ⅲ　Building up Ω　1. Finite fields  　Exercises　2. Extension of norms  　Exercises　3. The algebraic closure of Qp　4. Ω　　ExercisesChapter Ⅳ　p-adic power series　1. Elementary functions　　Exercises　2. The logarithm, gamma and Artin-Hasse exponential functions　　Exercises　3. Newton polygons for polynomials　4. Newton polygons for power series　　ExercisesChapter Ⅴ　Rationality of the zeta-function of a set of equations over a finite field　1. Hypersurfaces and their zeta-functions　　Exercises　2. Characters and their lifting　3. A linear map on the vector space of power series　4. p-adic analytic expression for the zeta-function　　Exercises　5. The end of the proofBibliographyAnswers and Hints for the ExercisesIndex

用户评论 (总计2条)

•   不错的GTM书，值得收藏和拥有！
•   很好，证明都不错，看了一半，感觉很好