p-Adic Methods and Their Applications [Hardcover]

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.

1. The Gray Code Function,F. Clarke
2. Applications of p-Adic Methods to Group Theory,M.P.F. Du Sautoy
3. Applications of the p-Adic Subspace Theorem,G.R. Everest
4. Out of the p-Acid into the Real Manchester School of p-Adic Analysis
5. Coupling Constants for p-Adic Groups,R.J. Plymen
6. The Local Fermat Problem,P. Ribenboim
7. L-Functions and Representation Theory of p-Adic Groups,F. Shahidi
8. Iwasawa Theory, Factorizability and the Galois Module Structure of Units,D.R. Solom
9. Weak Forms of Amenability for Split Rank 1 p-Adic Groups,A. Valette
10. p-Adic Fourier Series,C.F. Woodcock