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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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
1980
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| Schriftenreihe: | London Mathematical Society lecture note series
46 |
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| 520 | |a 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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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
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| isbn | 9780511526107 |
| language | English |
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| series2 | London Mathematical Society lecture note series |
| spelling | Koblitz, Neal 1948- Verfasser aut P-adic analysis a short course on recent work Neal Koblitz Cambridge Cambridge University Press 1980 1 online resource (163 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 46 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 p-adic analysis p-adische Zahl (DE-588)4044292-5 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-28060-0 https://doi.org/10.1017/CBO9780511526107 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Koblitz, Neal 1948- P-adic analysis a short course on recent work p-adic analysis p-adische Zahl (DE-588)4044292-5 gnd |
| subject_GND | (DE-588)4044292-5 |
| title | P-adic analysis a short course on recent work |
| title_auth | P-adic analysis a short course on recent work |
| title_exact_search | P-adic analysis a short course on recent work |
| title_full | P-adic analysis a short course on recent work Neal Koblitz |
| title_fullStr | P-adic analysis a short course on recent work Neal Koblitz |
| title_full_unstemmed | P-adic analysis a short course on recent work Neal Koblitz |
| title_short | P-adic analysis |
| title_sort | p adic analysis a short course on recent work |
| title_sub | a short course on recent work |
| topic | p-adic analysis p-adische Zahl (DE-588)4044292-5 gnd |
| topic_facet | p-adic analysis p-adische Zahl |
| url | https://doi.org/10.1017/CBO9780511526107 |
| work_keys_str_mv | AT koblitzneal padicanalysisashortcourseonrecentwork |