P-Adic Methods and Their Applications

ISBN-13: 9780198535942 / Angielski / Twarda / 1992 / 208 str.

Andrew J. Baker; Roger J. Plymen

Opis

The p-adic numbers and more generally local fields have become increasingly important in a wide range of mathematical disciplines. They are now seen as essential tools in many areas, including number theory, algebraic geometry, group representation theory, the modern theory of automorphic forms, and algebraic topology. A number of texts have recently become available which provide good general introductions to p-adic numbers and p-adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf by providing a collection of intermediate level articles on various applications of p-adic techniques throughout mathematics. The chapters will be especially useful for graduate students beginning research in these areas, and the contributors have been encouraged to write at a level suitable for this purpose.

Spis treści

Preface; Dedication to the memory of K. Mahler; Conventions and notations;Francis Clarke: The Gray Code Function; Marcus P.F. Du Sautoy: Applications of p-Adic methods to group theory; G.R. Everest: Applications of the p-Adic subspace theorem; Manchester School of P-Adic Analysis: Out of the p-Adic into the real; R.J. Plymen: Coupling constants for p-Adic groups; Paulo Ribenboim: The local fermat problem; Freydoon Shahidi: L-Functions and representation of p-Adic groups; David R. Solom: Iwasawa theory, factorizability and the Galois module structure of units; Alain Valette: Weak forms of amenability for split rank 1 p-Adic groups; C.F. Woodcock: p-Adic Fourier series.