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

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