Logo - springer
Slogan - springer

Mathematics - Number Theory and Discrete Mathematics | Number Theory I - Fundamental Problems, Ideas and Theories

Number Theory I

Fundamental Problems, Ideas and Theories

Manin, Yu. I., Panchishkin, Alexei A.

Original Russian edition published by VINITI, Moscow 1990

1995, V, 306 p.

eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

(net) price for USA

ISBN 978-3-662-08005-4

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

$69.99
  • Covers the most recent results around Fermat's Theorem (Andrew Wiles) and the Langlands Conjecture (Lafforgue)
This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry

Content Level » Research

Keywords » Arakelov geometry - Arithmetic der algebraischen Zahlen - Elementare Zahlentheorie - Elementary number theory - Langlands program - Langlands-Programm - Modular forms - Non-commutative geometry - arithmetic of algebraic numbers - diophantine equations - diophantische Gleichungen - elliptic curves - elliptische Kurven - logic - public - public key Verschlüsselungssysteme - public key cryptosystems - zeta-functions

Related subjects » Algebra - Mathematics - Number Theory and Discrete Mathematics - Security and Cryptology - Theoretical, Mathematical & Computational Physics

Table of contents 

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.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Number Theory.

Additional information