Introduction to P-Adic Analytic Number Theory

Maruti Ram Murty

ISBN 10: 082183262X / ISBN 13: 9780821832622

Edité par Amer Mathematical Society, Providence, RI, 2002

A propos de cet article

149 pages; Very Good condition. No noteworthy defects. No markings.; - Your satisfaction is our priority. We offer free returns and respond promptly to all inquiries. Your item will be carefully cushioned in bubble wrap and securely boxed. All orders ship on the same or next business day. Buy with confidence.

N° de réf. du vendeur GHC13-40876-OS-0

Détails bibliographiques

• Titre: Introduction to P-Adic Analytic Number Theory
• Éditeur: Amer Mathematical Society, Providence, RI
• Date de parution: 2002
• Langue: anglais
• ISBN à 10 chiffres: 082183262X
• ISBN à 13 chiffres: 9780821832622
• Reliure: Hardcover
• Édition: First Edition; First Printing.
• État de l'article: Very Good+
• État de la jaquette: No Dust Jacket As Issued

A propos de ce titre

Synopsis

This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises, it will acquaint the non-expert with the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences.These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory. The book treats the subject informally, making the text accessible to non-experts. It would make a nice independent text for a course geared toward advanced undergraduates and beginning graduate students.