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170324 ||| eng |
| 020 |
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|a 9780511526107
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| 050 |
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4 |
|a QA241
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|a Koblitz, Neal
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| 245 |
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|a P-adic analysis
|b a short course on recent work
|c Neal Koblitz
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 1980
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| 300 |
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|a 163 pages
|b digital
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| 653 |
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|a p-adic analysis
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
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|a London Mathematical Society lecture note series
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| 856 |
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|u https://doi.org/10.1017/CBO9780511526107
|x Verlag
|3 Volltext
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|a 512.74
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| 520 |
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|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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