Irrationality And Transcendence In Number Theory
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Irrationality And Transcendence In Number Theory
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Author : David Angell
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Irrationality And Transcendence In Number Theory written by David Angell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material. Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background
Irrationality And Transcendence In Number Theory
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Author : David Angell
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Irrationality And Transcendence In Number Theory written by David Angell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material. Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates. Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background.
Number Theory Iv
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Author : А. Н Паршин
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Number Theory Iv written by А. Н Паршин and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Transcendence In Algebra Combinatorics Geometry And Number Theory
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Author : Alin Bostan
language : en
Publisher: Springer Nature
Release Date : 2021-11-02
Transcendence In Algebra Combinatorics Geometry And Number Theory written by Alin Bostan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Number Theory Iv
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Author : A.N. Parshin
language : en
Publisher: Springer
Release Date : 1997-10-06
Number Theory Iv written by A.N. Parshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-06 with Mathematics categories.
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.
Pillars Of Transcendental Number Theory
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Author : Saradha Natarajan
language : en
Publisher: Springer Nature
Release Date : 2020-05-02
Pillars Of Transcendental Number Theory written by Saradha Natarajan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-02 with Mathematics categories.
This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.
Analytic Number Theory
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Author : W. W. L. Chen
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-19
Analytic Number Theory written by W. W. L. Chen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-19 with Mathematics categories.
A collection of papers inspired by the work of Britain's first Fields Medallist, Klaus Roth.
Number Theory Iv
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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Number Theory Iv written by A.N. Parshin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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 . . . . .
Continued Fractions From Analytic Number Theory To Constructive Approximation
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Continued Fractions From Analytic Number Theory To Constructive Approximation written by Bruce C. Berndt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.
Topics In Number Theory Volumes I And Ii
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Author : William J. LeVeque
language : en
Publisher: Courier Corporation
Release Date : 2012-06-22
Topics In Number Theory Volumes I And Ii written by William J. LeVeque and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-22 with Mathematics categories.
Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.