《P進數，P進分析和ζ函式》是2009年6月世界圖書出版公司出版的圖書，作者是科比利茲。本書可供數學係數論專業的研究生和研究人員參考。
基本介紹
- 書名：P進數，P進分析和ζ函式
- 作者：科比利茲
- ISBN：9787510004537
- 頁數：150
- 定價：25.00元
- 出版社：世界圖書出版公司
- 出版時間：2009-6
- 叢書： Graduate Texts in Mathematics
內容簡介,圖書目錄,
內容簡介
《P進數,P進分析和ζ函式(第2版)(英文版)》講述了：在數論，表示理論等許多現代數學研究領域中，p進分析占據著非常重要的地位。《P進數,P進分析和ζ函式(第2版)(英文版)》是p進分析的入門教材。主要分兩部分內容，首先論述p進分析理論的基本思想，其次介紹p進理論的兩個重要套用，即在黎曼ζ函式值為負整數時的p進內插和在一個有限域內方程組的δ函式有理性的證明。
圖書目錄
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
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
