LMS: 46 P Adic Analysis: A Short Course on Recent Work (London Mathematical Society Lecture Note Series)

Koblitz

ISBN 10: 0521280605 / ISBN 13: 9780521280600

Editore: Cambridge University Press 2008-01-12, 2008

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Codice articolo 6666-IUK-9780521280600

Dati bibliografici

• Titolo: LMS: 46 P Adic Analysis: A Short Course on Recent Work (London Mathematical Society Lecture Note Series)
• Editore: Cambridge University Press 2008-01-12
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0521280605
• ISBN 13: 9780521280600
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

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.

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.