| Description |
1 online resource (163 pages) |
| Series |
London Mathematical Society lecture note series ; 46, 0076-0552 |
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London Mathematical Society lecture note series ; 46.
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| Contents |
Cover; Half-title; Title; Copyright; Contents; Preface; CHAPTER I. BASICS; 1. History (very brief); 2. Basic concepts; 3. Power series; 4. Newton polygons; CHAPTER II. p-ADIC C-FUNCTIONS, L-FUNCTIONS AND r-FUNCTIONS; 1. Dirichlet L-series; 2. p-adic measures; 3. p-adic interpolation; 4. p-adic Dirichlet L-functions; 5. Leopoldt's formula for L (1,X); 6. The p-adic gamma function; 7. The p-adic log gamma function; 8. A formula for L'p(0,X); CHAPTER III. GAUSS SUMS AND THE p-ADIC GAMMA FUNCTION; 1. Gauss and Jacobi sums; 2. Fermat curves; 3. L-series for algebraic varieties; 4. Cohomology |
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5. p-adic cohomology6. p-adic formula for Gauss sums; 7. Stickleberger1s theorem; CHAPTER IV. p-ADIC REGULATORS; 1. Regulators and L-functions; 2. Leopoldt's p-adic regulator; 3. Gross's p-adic regulator; 4. Gross's conjecture in the abelian over Q case; APPENDIX; 1. A theorem of Amice-Fresnel; 2. The classical Stieltjes transform; 3. The Shnirelman integral and the p-adic Stieltjes transfonsfor; 4. p-adic spectral theorem; Bibliography; Index |
| Summary |
This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research |
| Bibliography |
Includes bibliographical references (pages 154-160) and index |
| Notes |
Print version record |
| Subject |
p-adic analysis.
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p-adic numbers.
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MATHEMATICS -- Number Theory.
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p-adic numbers
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p-adic analysis
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p-adische Zahl
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Analyse p-adique.
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| Form |
Electronic book
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| ISBN |
9781107361072 |
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1107361079 |
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9780511526107 |
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0511526105 |
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