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© LIBERO v6.4.1sp220816
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Catalogue Tag Display
MARC 21
Number Theory I: Fundamental Problems, Ideas and Theories
Tag
Description
020
$a9783662080054
082
$a512.7
099
$aOnline resource: Springer
245
$aNumber Theory I$h[EBook]$bFundamental Problems, Ideas and Theories$cedited by A. N. Parshin, I. R. Shafarevich.
260
$aBerlin, Heidelberg$bSpringer$c1995.
300
$aV, 306 pages$bonline resource.
336
$atext
338
$aonline resource
440
$aEncyclopaedia of Mathematical Sciences,$x0938-0396 ;$v49
505
$a
I. Problems and Tricks -- 1. Elementary Number Theory -- 2. Some Modern Problems of Elementary Number Theory -- II. Ideas and Theories -- 1. Induction and Recursion -- 2. Arithmetic of Algebraic Numbers -- 3. Arithmetic of Algebraic Varieties -- 4. Zeta Functions and Modular Forms -- References.
520
$a
This book 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 (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry.
538
$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700
$aParshin, A. N.$eeditor.
700
$aShafarevich, Igor R.(Igor Rostislavovich)$d1923-2017.$eeditor.
710
$aSpringerLink (Online service)
830
$aEncyclopaedia of Mathematical Sciences,$v49
856
$u
http://dx.doi.org/10.1007/978-3-662-08005-4
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