TY  - BOOK
AU  - Yuri Ivanovic Manin
AU  - Alexei A. Panchishkin
TI  - Introduction to modern number theory : : fundamental problems, ideas and theories
T2  -  Encyclopaedia of Mathematical Sciences
SN  - 9783540203643
AV  - QA241 
PY  - 2007///]
CY  - New York
PB  - Springer- Verlag
KW  - Arithmetic
N1  - 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])
N2  - "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
UR  - https://link.springer.com/book/10.1007/3-540-27692-0
ER  -