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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...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Cambridge [England] ; New York :
Cambridge University Press,
1980.
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| Collection: | London Mathematical Society lecture note series ;
46. |
| Sujets: | |
| Accès en ligne: | Texto completo |
| Résumé: | 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. |
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| Description matérielle: | 1 online resource (163 pages) |
| Bibliographie: | Includes bibliographical references (pages 154-160) and index. |
| ISBN: | 9781107361072 1107361079 9780511526107 0511526105 |
| ISSN: | 0076-0552 |