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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.
| Autorius: | Neal Koblitz |
| Leidėjas: | Cambridge University Press |
| Išleidimo metai: | 2004 |
| Knygos puslapių skaičius: | 168 |
| ISBN-10: | 0521280605 |
| ISBN-13: | 9780521280600 |
| Formatas: | 229 x 152 x 9 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „P-Adic Analysis: A Short Course on Recent Work“
