Coverart for item
The Resource Introduction to modern number theory : fundamental problems, ideas and theories, Yuri Ivanovic Manin, Alexei A. Panchishkin

Introduction to modern number theory : fundamental problems, ideas and theories, Yuri Ivanovic Manin, Alexei A. Panchishkin

Label
Introduction to modern number theory : fundamental problems, ideas and theories
Title
Introduction to modern number theory
Title remainder
fundamental problems, ideas and theories
Statement of responsibility
Yuri Ivanovic Manin, Alexei A. Panchishkin
Title variation
Number theory I
Creator
Contributor
Subject
Language
eng
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. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects. From the reviews of the 2nd edition: " ... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly up-to-date ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Manin, I︠U︡. I
Dewey number
512.7
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA241
LC item number
.M262 2005eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Panchishkin, A. A.
Series statement
Encyclopaedia of mathematical sciences,
Series volume
v. 49
http://library.link/vocab/subjectName
  • Number theory
  • Nombres, Théorie des
  • MATHEMATICS
  • Number theory
  • Getaltheorie
  • Variedades abelianas
  • Geometria algébrica
Label
Introduction to modern number theory : fundamental problems, ideas and theories, Yuri Ivanovic Manin, Alexei A. Panchishkin
Instantiates
Publication
Note
  • Rev. and updated version of Number theory I
  • First ed. originally issued as: Teorii︠a︡ chisel 1, v. 49 of the serial: Itogi i nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡
Bibliography note
Includes bibliographical references (pages 461-502) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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])
Control code
262680604
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xv, 514 pages)
Form of item
online
Isbn
9783540203643
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/3-540-27692-0
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-20364-3
Specific material designation
remote
System control number
(OCoLC)262680604
Label
Introduction to modern number theory : fundamental problems, ideas and theories, Yuri Ivanovic Manin, Alexei A. Panchishkin
Publication
Note
  • Rev. and updated version of Number theory I
  • First ed. originally issued as: Teorii︠a︡ chisel 1, v. 49 of the serial: Itogi i nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡
Bibliography note
Includes bibliographical references (pages 461-502) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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])
Control code
262680604
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xv, 514 pages)
Form of item
online
Isbn
9783540203643
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/3-540-27692-0
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-20364-3
Specific material designation
remote
System control number
(OCoLC)262680604

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