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
