Transcendental Numbers


Book Description

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.







Irrationality and Transcendence in Number Theory


Book Description

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


Book Description

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.




Contributions to the Theory of Transcendental Numbers


Book Description

Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.




Transcendental Numbers


Book Description

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.




Introduction to Algebraic Independence Theory


Book Description

In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.




Transcendental Number Theory


Book Description

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.




Making Transcendence Transparent


Book Description

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.




Introduction to Number Theory


Book Description

To Number Theory Translated from the Chinese by Peter Shiu With 14 Figures Springer-Verlag Berlin Heidelberg New York 1982 HuaLooKeng Institute of Mathematics Academia Sinica Beijing The People's Republic of China PeterShlu Department of Mathematics University of Technology Loughborough Leicestershire LE 11 3 TU United Kingdom ISBN -13 : 978-3-642-68132-5 e-ISBN -13 : 978-3-642-68130-1 DOl: 10.1007/978-3-642-68130-1 Library of Congress Cataloging in Publication Data. Hua, Loo-Keng, 1910 -. Introduc tion to number theory. Translation of: Shu lun tao yin. Bibliography: p. Includes index. 1. Numbers, Theory of. I. Title. QA241.H7513.5 12'.7.82-645. ISBN-13:978-3-642-68132-5 (U.S.). AACR2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustra tions, broadcasting, reproductiOli by photocopying machine or similar means, and storage in data banks. Under {sect} 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "VerwertungsgeselIschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1982 Softcover reprint of the hardcover 1st edition 1982 Typesetting: Buchdruckerei Dipl.-Ing. Schwarz' Erben KG, Zwettl. 214113140-5432 I 0 Preface to the English Edition The reasons for writing this book have already been given in the preface to the original edition and it suffices to append a few more points