Number Theory IV

Transcendental Numbers

A.N. Parshin, I.R. Shafarevich (Herausgeber)

Buch | Hardcover

VII, 345 Seiten

1997 | 1998
Springer Berlin (Verlag)
978-3-540-61467-8 (ISBN)

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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 . . . . .

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.

Erscheint lt. Verlag	6.10.1997
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	N.I. Fel'dman, Yu.V. Nesterenko
Übersetzer	N. Koblitz
Zusatzinfo	VII, 345 p.
Verlagsort	Berlin
Sprache	englisch
Maße	156 x 234 mm
Gewicht	648 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	analytic function • Approximation • Construction • DEX • differential equation • Equation • Function • Functions • Number Theory • Proof • slate • special function • techniques • Transcendental numbers • Transzendentale Zahlen • Zahlentheorie
ISBN-10	3-540-61467-2 / 3540614672
ISBN-13	978-3-540-61467-8 / 9783540614678
Zustand	Neuware