Yuri Ivanovic Manin

Introduction to modern number theory : fundamental problems, ideas and theories - 2nd Ed. - New York: Springer- Verlag, [c2007] - 514 p - Encyclopaedia of Mathematical Sciences Vol. 49 .

Part -I Problems and Tricks
1. Elementary Number Theory
2. Some Applications of Elementary Number Theory

Part - II Ideas and Theories
3. Induction and Recursion
4. Arithmetic of algebraic numbers
5. Arithmetic of algebraic varieties
6. Zeta Functions and Modular Forms
7. Fermat’s Last Theorem and Families of Modular Forms

Part - III Analogies and Visions
8. Introductory survey to part III: motivations and description
9. Arakelov Geometry and Noncommutative Geometry (d’après C. Consani and M. Marcolli, [CM])

"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 non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. --- summary provided by publisher

9783540203643


Arithmetic

QA241