Koblitz, Neal,
P-adic Analysis : A Short Course on Recent Work / Neal Koblitz. - Cambridge : Cambridge University Press, 1980. - 1 online resource (168 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 46 . - London Mathematical Society Lecture Note Series ; no. 46. .
Title from publisher's bibliographic system (viewed on 16 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.
9780511526107 (ebook)
p-adic analysis
QA241 / .K673
512/.74
P-adic Analysis : A Short Course on Recent Work / Neal Koblitz. - Cambridge : Cambridge University Press, 1980. - 1 online resource (168 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 46 . - London Mathematical Society Lecture Note Series ; no. 46. .
Title from publisher's bibliographic system (viewed on 16 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.
9780511526107 (ebook)
p-adic analysis
QA241 / .K673
512/.74