LMS: 46 P Adic Analysis: A Short Course on Recent Work - Brossura

Koblitz

Brossura

ISBN 10: 0521280605 ISBN 13: 9780521280600

Casa editrice: Cambridge University Press, 2008

Riassunto

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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Descrizione del libro

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 author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration.

Contenuti

Preface; 1. Basics; 2. p-adic functions, l-functions and r-functions; 3. Gauss sums and the p-adic gamma function; 4. p-adic regulators; Appendix; Bibliography; Index.

Dettagli dell'edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0521280605
• ISBN 13: 9780521280600
• Rilegatura: Copertina flessibile
• Numero di pagine: 168
• Contatto del produttore: non disponibile
• Persona responsabile: Avery; https://www.avery.fr/; ; chemin des peupliers 27; Dardilly; Francia