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＜電子ブック＞
Number Theory IV : Transcendental Numbers / edited by A.N. Parshin, I.R. Shafarevich
(Encyclopaedia of Mathematical Sciences ; 44)

版	1st ed. 1998.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1998
本文言語	英語
大きさ	VII, 345 p : online resource
冊子体	Transcendental numbers / A.N. Parshin, I.R. Shafarevich (eds.) ; : gw
著者標目	Parshin, A.N editor Shafarevich, I.R editor SpringerLink (Online service)
件　名	LCSH:Number theory FREE:Number Theory
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-03644-0

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