Non-Archimedean analytic functions, measures and distributions

Courtieu M., Panchishkin A.A.

Table of contents :
1.1.1 $p$-adic numbers……Page 1
1.1.3 The structure of the multiplicative group ${mathbb Q}^times_p$ and $K^times$……Page 3
1.1.5 The Tate field……Page 4
1.2.1 Continuous functions……Page 5
1.2.2 Analytic functions and power series……Page 6
1.2.3 Newton polygons……Page 8
1.3.1 Distributions……Page 9
1.3.2 Measures……Page 12
1.3.3 The $S$-adic Mazur measure……Page 14
1.4.1 The domain of definition of the non-Archimedean zeta functions……Page 16
1.4.2 The analytic structure of $X_S$……Page 17
1.4.3 The non-Archimedean Mellin transform……Page 19
1.4.4 The Iwasawa algebra……Page 20
1.4.5 Formulas for coefficients of power series……Page 21
1.4.6 Example. The $S$-adic Mazur measure and the non-Archimedean Kubota-Leopoldt zeta function……Page 22
1.5.1 Non-Archimedean integration……Page 23
1.5.2 $h$-admissible measure……Page 25
1.6.1 Dirichlet series……Page 26
1.6.2 Concluding remarks……Page 32