01638nmm a2200241 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001000139100001800149245006500167260004800232300002300280653002000303041001900323989003200342490005200374856006300426082001100489520089600500EB001382305EBX0100000000000000090527000000000000000.0cr|||||||||||||||||||||170324 ||| eng a9780511526107 4aQA2411 aKoblitz, Neal00aP-adic analysisba short course on recent workcNeal Koblitz aCambridgebCambridge University Pressc1980 a163 pagesbdigital ap-adic analysis07aeng2ISO 639-2 bCBOaCambridge Books Online0 aLondon Mathematical Society lecture note series uhttps://doi.org/10.1017/CBO9780511526107xVerlag3Volltext0 a512.74 aThis 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