P-adic Numbers. - An Introduction, 2nd Edition

There are numbers of all kinds: rational, real, complex, p-adic... The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students. This book can almost be viewed as an introduction to be read in preparation for reading these more advanced texts. Readers who want to have an idea and appreciation of the subject but do not need to become specialists will probably find what they need in this book, while other texts may be too technical. In this second edition the treatment of the p-adic logarithm and exponential functions has been modified to put more emphasis in the properties of functions defined by power series and to highlight the subtleties that arise when one considers the composition of formal power series in a non-archimedian context. The text and the exercises have been revised and partly reorganised; among the new exercises added one points towards Mahlers'p-adic interpolation theory.