000			03633nam a22005655i 4500
001			978-3-540-27692-0
003			DE-He213
005			20161121230933.0
007			cr nn 008mamaa
008			130729s2005 gw | s |||| 0|eng d
020			_a9783540276920 _9978-3-540-27692-0
024	7		_a10.1007/3-540-27692-0 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aManin, Yuri Ivanovic. _eauthor.
245	1	0	_aIntroduction to Modern Number Theory _h[electronic resource] : _bFundamental Problems, Ideas and Theories / _cby Yuri Ivanovic Manin, Alexei A. Panchishkin.
250			_a2.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2005.
300			_aXVI, 514 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aEncyclopaedia of Mathematical Sciences, _x0938-0396 ; _v49
505	0		_aProblems 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]).
520			_a"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).
650		0	_aMathematics.
650		0	_aData encryption (Computer science).
650		0	_aAlgebraic geometry.
650		0	_aMathematical logic.
650		0	_aNumber theory.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aMathematical Logic and Foundations.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aData Encryption.
650	2	4	_aNumerical and Computational Physics.
700	1		_aPanchishkin, Alexei A. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540203643
830		0	_aEncyclopaedia of Mathematical Sciences, _x0938-0396 ; _v49
856	4	0	_uhttp://dx.doi.org/10.1007/3-540-27692-0
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506150 _d506150