2009, ISBN: 9787030235084

hardcover. New. Ship out in 2 business day, And Fast shipping, Free Tracking number will be provided after the shipment.HardCover Pub Date: 2009 Pages: 345 Language: English Publisher: S… Mehr…

hardcover. New. Ship out in 2 business day, And Fast shipping, Free Tracking number will be provided after the shipment.HardCover Pub Date: 2009 Pages: 345 Language: English Publisher: Science Press. Number Theory: Beyond the number of (photocopy) is a survey of the most important directions Getting of research in transcendental number theory The central topics in this theory include proofs of irrationality and transcendence of various numbers. especially those. that arise as the values ??of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle. which Lindemann showed to bc impossible in 1882. when hc proved that Pi is a trandental number. Eulers conjecture that the logarithm of an algeaic number to an algeaic base is transcendental was included in Hilberts famous list of open problems; this conjecture was proved by Gelfond and Schneider in 1934. A more recent result was Anervs surprising proof of the irrationality of (3) in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different anches of number theory. this monograph provides both an overview of the central ideas and techniques of transcendental number theory. and also a guide to the most important results and references. Contents: NotationIntroduction0.1 Preliminary Remarks0.2 Irrationality of 20.3 The Number 0.4 Transcendental Numbers0 .5 Approximation of Algeaic Numbers0.6 Transcendence Questions and Other anches of Number Theory0.7 The Basic Problems Studied in Transcendental Number Theory0.8 Different Ways of Giving the Numbers0.9 MethodsChapter 1 Approximation of Algeaic Numbers1 Preliminaries 1.1 Parameters for Algeaic Numbers and Polynomials1 .2 Statement of the Problem1.3 Approximation of Rational Numbers1.4 Continued Fractions1.5 Quadratic Irrationalities1.6 Liouvilles Theorem and Liouville Numbers1.7 Generalization of Liouvilles Theorem2 Approximations of Algeaic Numbers and Thues Equation2.1 Thues Equation2.2 The Case n = 22.3 The Case n 33 Strengthening Liouvilles Theorem First Version of Thues Method3.1 A Way to Bound q-3.2 Construction of Rational Approximations for3.3 Thues First Result3.4 Effectiveness3.5 Effective Analogues of Theorem 1.63.6 The First Effective Inequalities of Baker3.7 Effective Bounds on Linear Forms in Algeaic Numbers4 Stronger and More General Versions of Liouvilles Theorem and Thues Theorem4.1 The Dirichlet Pigeonhole Principle4.2 Thues Method in the General Case4.3 Thues Theorem on Approximation of Algeaic Numbers4.4 The Non -effectiveness of Thues Theorems5 Further Development of Thues Method5.1 Siegels Theorem5.2 The Theorems of Dyson and Gelfond5.3 Dysons Lemma5.4 Bombieris Theorem6 Multidimensional Variants of the Thue-Siegel Method6.1 Preliminary Remarks6.2 Siegels Theorem6.3 The Theorems of Schneider and Mahler7 Roths Theorem7.1 Statement of the Theorem7.2 The Index of a Polynomial7.3 Outline of the Proof of Roths Theorem7.4 Approximation of Algeaic Numbers by Algeaic Numbers7.5 The Number k in Roths Theorem7.6 Approximation by Numbers of a Special Type7.7 Transcendence of Certain Numbers7.8 The Number of Solutions to the Inequality (62) and Certain Diophantine Equations8 Linear Forms in Algeaic Numbers and Schmidts Theorem8.1 Elementary Estimates8.2 Schmidts Theorem8.3 Minkowskis Theorem on Linear Forms8. 4 Schmidts Subspace TheoremChapter 2 Effective Constructions in Transcendental Number TheoryChapter 3 Hillberts Seventh ProblemChapter 4 Multidimensional Generalization of Hillberts Seventh ProblemChapter 5 Values ??of Analytic Functions That Satisgy Linear Differential EquationsChapter 6 Algeaic Independence of the Values ??of Analytic Functions That Have an Additaon La Satisfaction guaranteed,or money back.<

ISBN: 7030235088

Paperback, [EAN: 9787030235084], Science Press, Science Press, Book, [PU: Science Press], Science Press, 1025612, Subjects, 349777011, Antiquarian, Rare & Collectable, 91, Art, Architectu… Mehr…

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ISBN: 7030235088

Paperback, [EAN: 9787030235084], Science Press, Science Press, Book, [PU: Science Press], Science Press, 1025612, Subjects, 349777011, Antiquarian, Rare & Collectable, 91, Art, Architectu… Mehr…

Paperback, [EAN: 9787030235084], Science Press, Science Press, Book, [PU: Science Press], Science Press, 1025612, Subjects, 349777011, Antiquarian, Rare & Collectable, 91, Art, Architecture & Photography, 67, Biography, 68, Business, Finance & Law, 507848, Calendars, Diaries, Annuals & More, 69, Children's Books, 274081, Comics & Graphic Novels, 71, Computing & Internet, 72, Crime, Thrillers & Mystery, 62, Fiction, 66, Food & Drink, 275835, Gay & Lesbian, 74, Health, Family & Lifestyle, 65, History, 64, Home & Garden, 63, Horror, 89, Humour, 275738, Languages, 61, Mind, Body & Spirit, 73, Music, Stage & Screen, 275389, Poetry, Drama & Criticism, 59, Reference, 58, Religion & Spirituality, 88, Romance, 5106747031, School Books, 57, Science & Nature, 4034595031, Science Fiction & Fantasy, 564334, Scientific, Technical & Medical, 60, Society, Politics & Philosophy, 55, Sports, Hobbies & Games, 83, Travel & Holiday, 52, Young Adult, 266239, Books<

ISBN: 7030235088

Paperback, [EAN: 9787030235084], Science Press, Science Press, Book, [PU: Science Press], Science Press, 1025612, Subjects, 349777011, Antiquarian, Rare & Collectable, 91, Art, Architectu… Mehr…

Paperback, [EAN: 9787030235084], Science Press, Science Press, Book, [PU: Science Press], Science Press, 1025612, Subjects, 349777011, Antiquarian, Rare & Collectable, 91, Art, Architecture & Photography, 67, Biography, 68, Business, Finance & Law, 507848, Calendars, Diaries, Annuals & More, 69, Children's Books, 274081, Comics & Graphic Novels, 71, Computing & Internet, 72, Crime, Thrillers & Mystery, 279254, Fantasy, 62, Fiction, 66, Food & Drink, 275835, Gay & Lesbian, 74, Health, Family & Lifestyle, 65, History, 64, Home & Garden, 63, Horror, 89, Humour, 275738, Languages, 61, Mind, Body & Spirit, 73, Music, Stage & Screen, 275389, Poetry, Drama & Criticism, 59, Reference, 58, Religion & Spirituality, 88, Romance, 57, Science & Nature, 279292, Science Fiction, 564334, Scientific, Technical & Medical, 60, Society, Politics & Philosophy, 55, Sports, Hobbies & Games, 13384091, Study Books, 83, Travel & Holiday, 266239, Books<