A Short Course on Recent Work
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P-adic Analysis by Neal Koblitz
Book DescriptionThis 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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Book DetailsISBN: 9780521280600
(228mm x 152mm x 10mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 28-Nov-1980
Country of Publication: United Kingdom
Books By Author Neal Koblitz
P-adic Numbers, P-adic Analysis, and Zeta-functions, Hardback (April 1996)
This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-function, plus new exercises and an appendix of answers and hints.
Introduction to Elliptic Curves and Modular Forms, Hardback (April 1993)» View all books by Neal Koblitz
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book covers such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. It details the state of knowledge of elliptic curves.
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