Number Theory IV: Transcendental Numbers: 44 (Encyclopaedia of Mathematical Sciences) - Hardcover
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This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.
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Über die Autorin bzw. den Autor
Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.
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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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Number Theory IV
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Buch. Zustand: Neu. Neuware -This book was written over a period of more than six years. Several months after we finished our work, N.1. Fel'dman (the senior author of the book) died. All additions and corrections entered after his death were made by his coauthor. The assistance of many of our colleagues was invaluable during the writing of the book. They examined parts of the manuscript and suggested many improvements, made useful comments and corrected many errors. I much have pleasure in acknowledging our great indebtedness to them. Special thanks are due to A. B. Shidlovskii, V. G. Chirskii, A.1. Galochkin and O. N. Vasilenko. I would like to express my gratitude to D. Bertrand and J. Wolfart for their help in the final stages of this book. Finally, I wish to thank Neal Koblitz for having translated this text into English. August 1997 Yu. V.Nesterenko Transcendental Numbers N.1. Fel'dman and Yu. V. Nesterenko Translated from the Russian by Neal Koblitz Contents Notation . 9 Introduction . 11 0.1 Preliminary Remarks . 11 0.2 Irrationality of J2 . 11 0.3 The Number 1C' ¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿ 13 0.4 Transcendental Numbers . 14 0.5 Approximation of Algebraic Numbers . 15 0.6 Transcendence Questions and Other Branches of Number Theory . 16 0.7 The Basic Problems Studied in Transcendental Number Theory . 17 0.8 Different Ways of Giving the Numbers . 19 0.9 Methods . . . . . . . . . . . . . . . 20 . . . . .Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 360 pp. Englisch. Artikel-Nr. 9783540614678
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Number Theory IV : Transcendental Numbers
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book was written over a period of more than six years. Several months after we finished our work, N.1. Fel'dman (the senior author of the book) died. All additions and corrections entered after his death were made by his coauthor. The assistance of many of our colleagues was invaluable during the writing of the book. They examined parts of the manuscript and suggested many improvements, made useful comments and corrected many errors. I much have pleasure in acknowledging our great indebtedness to them. Special thanks are due to A. B. Shidlovskii, V. G. Chirskii, A.1. Galochkin and O. N. Vasilenko. I would like to express my gratitude to D. Bertrand and J. Wolfart for their help in the final stages of this book. Finally, I wish to thank Neal Koblitz for having translated this text into English. August 1997 Yu. V.Nesterenko Transcendental Numbers N.1. Fel'dman and Yu. V. Nesterenko Translated from the Russian by Neal Koblitz Contents Notation . 9 Introduction . 11 0.1 Preliminary Remarks . 11 0.2 Irrationality of J2 . 11 0.3 The Number 1C' ---------------------------------------- 13 0.4 Transcendental Numbers . 14 0.5 Approximation of Algebraic Numbers . 15 0.6 Transcendence Questions and Other Branches of Number Theory . 16 0.7 The Basic Problems Studied in Transcendental Number Theory . 17 0.8 Different Ways of Giving the Numbers . 19 0.9 Methods . . . . . . . . . . . . . . . 20 . . . . . Artikel-Nr. 9783540614678
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