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Description
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.
Product details
- Type:
- Book
- Binding:
- Paperback
- Edition:
- 1
- Languages:
-
Original:
English
- Number of Pages:
-
168
- Publisher:
-
Cambridge University Press
- Publication Date:
-
2004-05-15
- Release Date:
-
2008-01-12
- ISBN / EAN:
-
088422186791497805212806009781845889111
- Weight:
-
254 g
- Dimensions:
-
15/23/1 cm
- GPSR Manufacturer Reference:
-
[email protected]
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