Introduction to modern number theory : fundamental problems, ideas and theories

By: Yuri Ivanovic ManinContributor(s): Alexei A. PanchishkinMaterial type: TextTextSeries: Encyclopaedia of Mathematical Sciences ; Vol. 49Publication details: New York: Springer- Verlag, [c2007]Edition: 2nd EdDescription: 514 pISBN: 9783540203643Subject(s): ArithmeticLOC classification: QA241Online resources: Click here to access online
Contents:
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])
Summary: "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
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 4 QA241 (Browse shelf (Opens below)) Available Invoice no. IN 7525 ; Date 15-03-2019 01825
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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

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