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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...

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Detalles Bibliográficos
Autor principal: Koblitz, Neal
Lenguaje:eng
Publicado: Cambridge University Press 1980
Materias:
Acceso en línea:http://cds.cern.ch/record/1619153
Descripción
Sumario: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.