000			04092nam a22005055i 4500
001			978-0-387-49923-9
003			DE-He213
005			20250710084005.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387499239 _a99780387499239
024	7		_a10.1007/978-0-387-49923-9 _2doi
082	0	4	_a512.7 _223
100	1		_aCohen, Henri. _eauthor.
245	1	0	_aNumber Theory _h[recurso electrónico] : _bVolume I: Tools and Diophantine Equations / _cby Henri Cohen.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aXXIII, 650 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v239
505	0		_ato Diophantine Equations -- to Diophantine Equations -- Tools -- Abelian Groups, Lattices, and Finite Fields -- Basic Algebraic Number Theory -- p-adic Fields -- Quadratic Forms and Local-Global Principles -- Diophantine Equations -- Some Diophantine Equations -- Elliptic Curves -- Diophantine Aspects of Elliptic Curves.
520			_aThe central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results.
650		0	_aMATHEMATICS.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aALGEBRA.
650		0	_aCOMPUTER SCIENCE _xMATHEMATICS.
650		0	_aALGORITHMS.
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aNUMBER THEORY.
650	2	4	_aALGORITHMS.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aCOMPUTATIONAL MATHEMATICS AND NUMERICAL ANALYSIS.
650	2	4	_aORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387499222
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v239
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-49923-9 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57896 _d57896