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001			00011870
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007			cr cnu|||unuuu
008			200906s2020 si ob 001 0 eng
040			_a WSPC _b eng _c WSPC
010			_z 2020027465
020			_a9789811221842 _q(ebook)
020			_z9789811221835 _q(hbk.)
050	0	4	_aQA567.2.E44 _bM55 2020
072		7	_aMAT _x022000 _2bisacsh
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072		7	_aMAT _x000000 _2bisacsh
082	0	4	_a516.3/52 _223
100	1		_aMilne, J. S., _d1942- _921218
245	1	0	_aElliptic curves _h[electronic resource] / _cby James S. Milne.
250			_a2nd ed.
260			_aSingapore : _bWorld Scientific, _c2020.
300			_a1 online resource (x, 308 p.)
504			_aIncludes bibliographical references and index.
520			_a"This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated"--Publisher's website.
505	0		_aAlgebraic curves -- Basic theory of elliptic curves -- Elliptic curves over the complex numbers -- The arithmetic of elliptic curves -- Elliptic curves and modular forms.
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat Reader.
650		0	_aCurves, Elliptic. _921219
655		0	_aElectronic books. _93294
856	4	0	_uhttps://www.worldscientific.com/worldscibooks/10.1142/11870#t=toc _zAccess to full text is restricted to subscribers.
942			_cEBK
999			_c72779 _d72779