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Author : Alan Baker
Publisher : Cambridge University Press
Page : 185 pages
File Size : 52,7 Mb
Release : 2022-06-09
Category : Computers
ISBN : 9781009229944
Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Author : M. Ram Murty,Purusottam Rath
Publisher : Springer
Page : 219 pages
File Size : 47,5 Mb
Release : 2014-06-24
Category : Mathematics
ISBN : 9781493908325
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 : David Angell
Publisher : CRC Press
Page : 243 pages
File Size : 45,6 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781000523737
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.
Author : Saradha Natarajan,Ravindranathan Thangadurai
Publisher : Springer Nature
Page : 184 pages
File Size : 41,8 Mb
Release : 2020-05-02
Category : Mathematics
ISBN : 9789811541551
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.
Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 42,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662036440
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 : Edward B. Burger,Robert Tubbs
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 52,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741148
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.
Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 55,8 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : Serge Lang
Publisher : Unknown
Page : 120 pages
File Size : 53,5 Mb
Release : 1966
Category : Transcendental numbers
ISBN : STANFORD:36105031201903
Author : Alan Baker
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,5 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009229968
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
Author : Gregory Chudnovsky
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 41,9 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821815007
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 : Michel Waldschmidt
Publisher : Springer Science & Business Media
Page : 649 pages
File Size : 51,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662115695
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.
Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer
Page : 345 pages
File Size : 50,7 Mb
Release : 1997-10-06
Category : Mathematics
ISBN : 3540614672
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 : Yuri V. Nesterenko,Patrice Philippon
Publisher : Springer
Page : 260 pages
File Size : 47,9 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540445500
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.
Author : Andrei B. Shidlovskii
Publisher : Walter de Gruyter
Page : 489 pages
File Size : 41,5 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110889055
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 : Harry Pollard,Harold G. Diamond
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 41,8 Mb
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 9781614440093
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.