P进数,P进分析和ζ函数
2009-6
世界图书出版公司
科比利兹
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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。
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
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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