Ultrametric Calculus
An Introduction to p-Adic Analysis

This is an introduction to p-adic analysis, displaying the variety of applications of the subject.

W. H. Schikhof (Author)

9780521032872, Cambridge University Press

Paperback / softback, published 25 January 2007

320 pages
22.8 x 15.2 x 2 cm, 0.471 kg

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.

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.

Subject Areas: Probability & statistics [PBT]