Non-Archimedean analytic functions, measures and distributions

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