Ultrametric calculus : an introduction to p-adic analysis
著者
書誌事項
Ultrametric calculus : an introduction to p-adic analysis
（Cambridge studies in advanced mathematics, 4）
Cambridge University Press, 1984
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注記
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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