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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1980.
|
| Colección: | London Mathematical Society lecture note series ;
46. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Koblitz, Neal, |d 1948- | |
| 245 | 1 | 0 | |a P-adic analysis : |b a short course on recent work / |c Neal Koblitz. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1980. | ||
| 300 | |a 1 online resource (163 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 46, |x 0076-0552 | |
| 504 | |a Includes bibliographical references (pages 154-160) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
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| 650 | 0 | |a p-adic analysis. | |
| 650 | 0 | |a p-adic numbers. | |
| 650 | 6 | |a Nombres p-adiques. | |
| 650 | 6 | |a Analyse p-adique. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a p-adic numbers. |2 fast |0 (OCoLC)fst01185030 | |
| 650 | 7 | |a p-adic analysis. |2 fast |0 (OCoLC)fst01185026 | |
| 650 | 7 | |a p-adische Zahl |2 gnd | |
| 650 | 7 | |a Analyse p-adique. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Koblitz, Neal, 1948- |t P-adic analysis. |d Cambridge [Eng.] ; New York : Cambridge University Press, 1980 |z 0521280605 |w (DLC) 80040806 |w (OCoLC)6602842 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 46. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552448 |z Texto completo |
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