%0 eBook
%M Solr-EB001382305
%A Koblitz, Neal
%I Cambridge University Press
%D 1980
%C Cambridge
%G English
%B London Mathematical Society lecture note series
%@ 9780511526107
%T P-adic analysis : a short course on recent work
%U https://doi.org/10.1017/CBO9780511526107
%X 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