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Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories

"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...

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Bibliographic Details
Main Authors: Manin, Yu. I., Panchishkin, Alexei A. (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005, 2005
Edition:2nd ed. 2005
Series:Encyclopaedia of Mathematical Sciences
Subjects:
Number Theory
Algebraic Geometry
Mathematical Logic
Cryptography
Data Encryption (computer Science)
Mathematical Physics
Cryptology
Mathematical Logic And Foundations
Theoretical, Mathematical And Computational Physics
Mathematical Methods In Physics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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])

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