TY - BOOK ID - 77894953 TI - P-adic analysis PY - 1980 VL - 46 SN - 00760552 SN - 1139883976 1107365988 110737071X 1107361079 1107368154 1299403794 1107363527 0511526105 9781107361072 9780511526107 0521280605 9780521280600 PB - Cambridge [England] New York Cambridge University Press DB - UniCat KW - p-adic analysis. KW - Analysis, p-adic KW - Algebra KW - Calculus KW - Geometry, Algebraic KW - p-adic analysis KW - #WWIS:d.d. Prof. L. Bouckaert/ALTO KW - 511.6 KW - 511.6 Algebraic number fields KW - Algebraic number fields KW - P-adic analysis. KW - Number theory UR - https://www.unicat.be/uniCat?func=search&query=sysid:77894953 AB - 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. ER -