Number Theory IV: Transcendental Numbers
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
44 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (VII, 345 p) |
| ISBN: | 9783662036440 9783642082597 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-03644-0 |
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| 500 | |a 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 | ||
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03644-0 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662036440 9783642082597 |
| issn | 0938-0396 |
| language | English |
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| spelling | Paršin, Aleksej Nikolaevič 1942-2022 Verfasser (DE-588)172519012 aut Number Theory IV Transcendental Numbers edited by A. N. Parshin, I. R. Shafarevich Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource (VII, 345 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 44 0938-0396 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 Mathematics Number theory Number Theory Mathematik Šafarevič, Igorʹ R. 1923-2017 Sonstige (DE-588)119280337 oth https://doi.org/10.1007/978-3-662-03644-0 Verlag Volltext |
| spellingShingle | Paršin, Aleksej Nikolaevič 1942-2022 Number Theory IV Transcendental Numbers Mathematics Number theory Number Theory Mathematik |
| title | Number Theory IV Transcendental Numbers |
| title_auth | Number Theory IV Transcendental Numbers |
| title_exact_search | Number Theory IV Transcendental Numbers |
| title_full | Number Theory IV Transcendental Numbers edited by A. N. Parshin, I. R. Shafarevich |
| title_fullStr | Number Theory IV Transcendental Numbers edited by A. N. Parshin, I. R. Shafarevich |
| title_full_unstemmed | Number Theory IV Transcendental Numbers edited by A. N. Parshin, I. R. Shafarevich |
| title_short | Number Theory IV |
| title_sort | number theory iv transcendental numbers |
| title_sub | Transcendental Numbers |
| topic | Mathematics Number theory Number Theory Mathematik |
| topic_facet | Mathematics Number theory Number Theory Mathematik |
| url | https://doi.org/10.1007/978-3-662-03644-0 |
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