A Course in p-adic AnalysisSpringer Science & Business Media, 31 mai 2000 - 438 pages Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements. |
Table des matières
The Compact Space | 7 |
Topological Algebra | 17 |
Hensels Philosophy | 45 |
Finite Extensions of the Field of padic Numbers | 69 |
FiniteDimensional Vector Spaces | 90 |
Structure of padic Fields | 97 |
Classification of Locally Compact Fields | 115 |
Locally Compact Vector Spaces Revisited | 121 |
Continuous Functions on Z | 160 |
Differentiation | 217 |
Analytic Functions and Elements | 280 |
Special Functions Congruences | 366 |
Specific References for the Text | 419 |
Tables | 425 |
Conventions Notation Terminology | 431 |
137 | |
Autres éditions - Tout afficher
Expressions et termes fréquents
absolute value algebraically closed analytic element Banach space binomial bounded co(I coefficients complete composition operator compute consider continuous function convergent power series Corollary critical radius defined definition delta operator denote differentiable Enzo example exp(x exponential extension of Qp formal power series formula function f growth modulus hence homomorphism inequality infraconnected inverse isomorphism Laurent series lemma Let f linear locally compact log(1+x logarithm Mahler series maximal monomials multiplicative neighborhood nonzero notation open ball p-adic Analysis p-adic integers poles polynomial prime PROOF Proposition proves quotient radius of convergence rational function residue field restricted ring roots of unity satisfies sequence series expansion shows sphere subgroup subset subspace surjective Theorem ultrametric field uniformly unique unit ball vector space zero