P-adic numbers

Includes index

Includes bibliography (p. 297-300) and references

1. Aperitif. 1.1. Hensel's analogy ; 1.2. Solving congruences modulo pn ; 1.3. Other examples
2. Foundations. 2.1. Absolute values on a field ; 2.2. Basic properties ; 2.3. Topology ; 2.4. Algebra
3. p-adic numbers. 3.1. Absolute values on Q ; 3.2. Completions ; 3.3. Exploring Qp ; 3.4. Hensel's lemma ; 3.5. Local and global
4. Elementary analysis in Qp. 4.1. Sequences and series ; 4.2. Power series ; 4.3. Some wlementary functions ; 4.4. Interpolation
5. Vector spaces and field extensions. 5.1. Normed vector spaces over complete valued fields ; 5.2. Finite-imensional normed vector spaces ; 5.3. Finite field extensions ; 5.4. Properties of finite extensions ; 5.5. Analysis ; 5.6. Example: adjoining a p-th root of unity ; 5.7. On to Cp
6. Analysis in Cp. 6.1. Almost everything extends ; 6.2. Derivatives ; 6.3. Deeper results on polynomials and power series ; 6.4. Entire functions ; 6.5. Newton polygons ; 6.6. Problems

There are numbers of all kinds: rational, real, complex, p-adic. This elementary introduction offers a broad understanding of p-adic numbers.From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is.