Manin / Panchishkin Number Theory I

Fundamental Problems, Ideas and Theories
1995
ISBN: 978-3-662-08005-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 49, 306 Seiten, eBook

Reihe: Encyclopaedia of Mathematical Sciences

A unified survey of both the status quo and the continuing trends of various branches of number theory. Motivated by elementary problems, the authors present todays most significant results and methods. Topics covered include non-Abelian generalisations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. The book is rounded off with an overview of the major conjectures, most of which are based on analogies between functions and numbers, and on connections with other branches of mathematics such as analysis, representation theory, geometry and algebraic topology.

Zielgruppe

Research

Autoren/Hrsg.

Manin, Yu. I.

Panchishkin, Alexei A.

Inhaltsverzeichnis

I. Problems and Tricks.- 1. Elementary Number Theory.- 2. Some Modern Problems of Elementary Number Theory.- II. Ideas and Theories.- 1. Induction and Recursion.- 2. Arithmetic of Algebraic Numbers.- 3. Arithmetic of Algebraic Varieties.- 4. Zeta Functions and Modular Forms.- References.