P进数,P进分析和ζ函数
实物如图,内页干净。323
¥
165
九品
库存2件
作者科比利兹
出版社世界图书出版公司
出版时间2009-06
版次1
装帧平装
上书时间2023-06-15
商品详情
- 品相描述:九品
图书标准信息
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作者
科比利兹
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出版社
世界图书出版公司
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出版时间
2009-06
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版次
1
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ISBN
9787510004537
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定价
25.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
- 【内容简介】
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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。
- 【目录】
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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
Exercises
Chapter 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)
Exercises
Chapter Ⅲ Building up Ω
1. Finite fields
Exercises
2. Extension of norms
Exercises
3. The algebraic closure of Qp
4. Ω
Exercises
Chapter 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
Exercises
Chapter 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 proof
Bibliography
Answers and Hints for the Exercises
Index
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