P進數,P進分析和ζ函式

P進數,P進分析和ζ函式

《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。

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 

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