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Author: Carl Ludwig Siegel
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 102
ISBN-13: 1400882354
DOWNLOAD EBOOK →The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.
Author: Andrei B. Shidlovskii
Publisher: Walter de Gruyter
Published: 2011-06-01
Total Pages: 489
ISBN-13: 3110889056
DOWNLOAD EBOOK →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.
Author: M. Ram Murty
Publisher: Springer
Published: 2014-06-24
Total Pages: 219
ISBN-13: 1493908324
DOWNLOAD EBOOK →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.
Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 464
ISBN-13: 0821815008
DOWNLOAD EBOOK →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.
Author: Władysław Narkiewicz
Publisher: Springer Science & Business Media
Published: 2011-09-02
Total Pages: 659
ISBN-13: 0857295322
DOWNLOAD EBOOK →The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Author: Robert Tubbs
Publisher: Springer
Published: 2016-11-23
Total Pages: 85
ISBN-13: 9811026459
DOWNLOAD EBOOK →This exposition is primarily a survey of the elementary yet subtle innovations of several mathematicians between 1929 and 1934 that led to partial and then complete solutions to Hilbert’s Seventh Problem (from the International Congress of Mathematicians in Paris, 1900). This volume is suitable for both mathematics students, wishing to experience how different mathematical ideas can come together to establish results, and for research mathematicians interested in the fascinating progression of mathematical ideas that solved Hilbert’s problem and established a modern theory of transcendental numbers.
Author: A.N. Parshin
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 351
ISBN-13: 3662036444
DOWNLOAD EBOOK →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.
Author: Alan Baker
Publisher: Cambridge University Press
Published: 2022-06-09
Total Pages: 185
ISBN-13: 100922994X
DOWNLOAD EBOOK →Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Author: Gisbert Wüstholz
Publisher: Springer
Published: 2006-11-15
Total Pages: 252
ISBN-13: 3540480234
DOWNLOAD EBOOK →Author: Saradha Natarajan
Publisher: Springer Nature
Published: 2020-05-02
Total Pages: 184
ISBN-13: 9811541558
DOWNLOAD EBOOK →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.
