Hjem

1 Ap?ritif. - 1 Ap?ritif. -
1.
1 Hensel's Analogy. -
1.
2 Solving Congruences Modulopn. -
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 '. -
3.
2 Completions. -
3.
3 Exploring ?p. -
3.
4 Hensel's Lemma. -
3.
5 Local and Global. - 4 Elementary Analysis in'p. -
4.
1 Sequences and Series. -
4.
2 Functions, Continuity, Derivatives. -
4.
3 Power Series. -
4.
4 Functions Defined by Power Series. -
4.
5 Some Elementary Functions. -
4.
6 Interpolation. - 5 Vector Spaces and Field Extensions. -
5.
1 Normed Vector Spaces over Complete Valued Fields. -
5.
2 Finite-dimensional 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 '. - 6 Analysis in'p. -
6.
1 Almost Everything Extends. -
6.
2 Deeper Results on Polynomials and Power Series. -
6.
3 Entire Functions. -
6.
4 Newton Polygons. -
6.
5 Problems. - A Hints and Comments on the Problems. - B A Brief Glance at the Literature. - B.
1 Texts. - B.
2 Software. - B.
3 Other Books.