Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories /

• Main Authors: Manin, Yuri Ivanovic (Author), Panchishkin, Alexei A. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
• Edition: 2.
• Series: Encyclopaedia of Mathematical Sciences, 49
• Subjects: Mathematics.; Data encryption (Computer science).; Algebraic geometry.; Mathematical logic.; Number theory.; Physics.; Number Theory.; Algebraic Geometry.; Mathematical Logic and Foundations.; Mathematical Methods in Physics.; Data Encryption.; Numerical and Computational Physics.

"Introduction to Modern Number Theory" 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, the central ideas of modern theories are exposed. Some topics covered include n...

Table of Contents:

• Problems and Tricks
• Number Theory
• Some Applications of Elementary Number Theory
• Ideas and Theories
• Induction and Recursion
• Arithmetic of algebraic numbers
• Arithmetic of algebraic varieties
• Zeta Functions and Modular Forms
• Fermat’s Last Theorem and Families of Modular Forms
• Analogies and Visions
• Introductory survey to part III: motivations and description
• Arakelov Geometry and Noncommutative Geometry (d’après C. Consani and M. Marcolli, [CM]).