P-adic analysis : a short course on recent work /
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 f...
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| Online Access: | Electronic book from EBSCO |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: | Cambridge [England] ; New York : Cambridge University Press, 1980. |
| Series: | London Mathematical Society lecture note series ;
46. |
| Subjects: |
Table of 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
- 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