Number Theory IV: Transcendental Numbers: Encyclopaedia of Mathematical Sciences, cartea 44
Editat de A.N. Parshin Traducere de N. Koblitz Contribuţii de N.I. Fel'dman Editat de I.R. Shafarevich Contribuţii de Yu.V. Nesterenkoen Limba Engleză Hardback – 6 oct 1997
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Specificații
ISBN-13: 9783540614678
ISBN-10: 3540614672
Pagini: 360
Ilustrații: VII, 345 p.
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.68 kg
Ediția:1998
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3540614672
Pagini: 360
Ilustrații: VII, 345 p.
Dimensiuni: 156 x 234 x 25 mm
Greutate: 0.68 kg
Ediția:1998
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
1. Approximation of Algebraic Numbers.- 2. Effective Constructions in Transcendental Number Theory.- 3. Hilbert’s Seventh Problem.- 4. Multidimensional Generalization of Hilbert’s Seventh Problem.- 5. Values of Analytic Functions That Satisfy Linear Differential Equations.- 6. Algebraic Independence of the Values of Analytic Functions That Have an Addition Law.
Textul de pe ultima copertă
This book is a survey of the most important directions 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 be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ 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 branches 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.