p-adic analysis

About: p-adic analysis is a research topic. Over the lifetime, 94 publications have been published within this topic receiving 4188 citations.

p-adic Numbers, p-adic Analysis, and Zeta-Functions

Abstract: P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).

A Course in p-adic Analysis

Abstract: 1 p-adic Numbers.- 2 Finite Extensions of the Field of p-adic Numbers.- 3 Construction of Universal p-adic Fields.- 4 Continuous Functions on Zp.- 5 Differentiation.- 6 Analytic Functions and Elements.- 7 Special Functions, Congruences.- Specific References for the Text.- Tables.- Basic Principles of Ultrametric Analysis.- Conventions, Notation, Terminology.

p-Adic Valued Distributions in Mathematical Physics

Abstract: Introduction. I. First Steps to Non-Archimedean Fields. II. The Gauss, Lebesgue and Feynman Distributions over Non-Archimedean Fields. III. The Gauss and Feynman Distributions on Infinite-Dimensional Spaces over Non-Archimedean Fields. IV. Quantum Mechanics for Non-Archimedean Wave Functions. V. Functional Integrals and the Quantization of Non-Archimedean Models with an Infinite Number of Degrees of Freedom. VI. The p-Adic-Valued Probability Measures. VII. Statistical Stabilization with Respect to p-Adic and Real Metrics. VIII. The p-Adic Valued Probability Distributions (Generalized Functions). IX. p-Adic Superanalysis. Bibliographical Remarks. Open Problems. Appendix: 1. Expansion of Numbers on a Given Scale. 2. An Analogue of Newton's Method. 3. Non-Existence of Differential Maps from Qp to R. Bibliography. Index.

Ultrametric calculus : an introduction to p-adic analysis

Abstract: Frontispiece Preface Part I. Valuations: 1. Valuations 2. Ultrametrics Part II. Calculus: 3. Elementary calculus 4. Interpolation 5. Analytic functions Part III. Functions on Zp: 6. Mahler's base and p-adic integration 7. The p-adic gamma and zeta functions 8. van der Put's base and antiderivation Part IV. More General Theory of Functions: 9. Continuity and differentiability 10. Cn -theory 11. Monotone functions Appendixes Further reading Notation Index.

Distribution Modulo One and Diophantine Approximation

Abstract: This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the distribution modulo one of the integral powers of 3/2 and the frequency of occurrence of each digit in the decimal expansion of the square root of two. The author takes a point of view from combinatorics on words and introduces a variety of techniques, including explicit constructions of normal numbers, Schmidt's games, Riesz product measures and transcendence results. With numerous exercises, the book is ideal for graduate courses on Diophantine approximation or as an introduction to distribution modulo one for non-experts. Specialists will appreciate the inclusion of over 50 open problems and the rich and comprehensive bibliography of over 700 references.