Transcendental And Algebraic Numbers
DOWNLOAD
Download Transcendental And Algebraic Numbers PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Transcendental And Algebraic Numbers book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Transcendental And Algebraic Numbers
DOWNLOAD
Author : A. O. Gelfond
language : en
Publisher: Courier Dover Publications
Release Date : 2015-01-05
Transcendental And Algebraic Numbers written by A. O. Gelfond and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-05 with Mathematics categories.
Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers. Topics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.
Transcendental Numbers
DOWNLOAD
Author : M. Ram Murty
language : en
Publisher: Springer
Release Date : 2014-06-24
Transcendental Numbers written by M. Ram Murty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-24 with Mathematics categories.
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Diophantine Approximation On Linear Algebraic Groups
DOWNLOAD
Author : Michel Waldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Diophantine Approximation On Linear Algebraic Groups written by Michel Waldschmidt 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 2013-03-14 with Mathematics categories.
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
Number Theory Iv
DOWNLOAD
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 . . . . .
Number Theory Iv
DOWNLOAD
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.
Irrationality And Transcendence In Number Theory
DOWNLOAD
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.
An Invitation To Modern Number Theory
DOWNLOAD
Author : Steven J. Miller
language : en
Publisher: Princeton University Press
Release Date : 2020-07-21
An Invitation To Modern Number Theory written by Steven J. Miller and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-21 with Mathematics categories.
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
The Theory Of Algebraic Numbers Second Edition
DOWNLOAD
Author : Harry Pollard
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
The Theory Of Algebraic Numbers Second Edition written by Harry Pollard 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 1975-12-31 with Mathematics categories.
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Wonders Of Numbers
DOWNLOAD
Author : Clifford A. Pickover
language : en
Publisher: Oxford University Press
Release Date : 2003-01-16
Wonders Of Numbers written by Clifford A. Pickover and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-16 with Mathematics categories.
Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.