Download or read book On the Algebraic Independence of Transcendental Numbers of Certain Classes written by Aleksandr Osipovich Gelʹfond and published by . This book was released on 1952 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transcendental Numbers written by M. Ram Murty and published by Springer. This book was released on 2014-06-24 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book On the Algebraic Independence of Trancendental Numbers of Certain Classes written by Aleksandr Osipovich Gelʹfond and published by . This book was released on 1952 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transcendence and Algebraic Independence Results for Certain Classes of U numbers written by Deanna Marie Caveny and published by . This book was released on 1991 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Algebraic Independence of Transcendental Numbers of Certain Clauses written by Aleksandr Osipovich Gelʹfond and published by . This book was released on 1952 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Transcendental Numbers written by Andrei B. Shidlovskii and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebraic Independence of the Values at Algebraic Points of a Class of Functions Considered by Mahler written by N. Ch Wass and published by . This book was released on 1990 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1,\... m)(\*)\cr} TABLE/EQUATION ENDS)for b $\geq$ 2, a$\sb{\rm ij}$(z), b$\sb{\rm j}$(z) in K(z). Suppose finally that $\alpha\in\kappa$ is such that 0 $

Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by Springer. This book was released on 2003-07-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Contributions to the Theory of Transcendental Numbers written by Gregory Chudnovsky and published by American Mathematical Soc.. This book was released on 1984 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Lectures on Transcendental Numbers written by K. Mahler and published by Springer. This book was released on 2006-11-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transcendental and Algebraic Numbers written by A. O. Gelfond and published by Courier Dover Publications. This book was released on 2015-01-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Download or read book Algebraic Independence written by I︠U︡riĭ Valentinovich Nesterenko and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the notes of a course of lectures given by at the Tata Institute of Fundamental Research in 1998. It deals with several important results and methods in transcendental number theory. First, the classical result of Lindemann-Weierstrass and its applications are dealt with. Subsequently, Siegel's theory of $E$-functions is developed systematically, culminating in Shidlovskii's theorem on the algebraic independence of the values of the $E$-functions satisfying a system of differential equations at certain algebraic values. Proof of the Gelfond-Schneider Theorem is given based on the method of interpolation determinants introduced in 1992 by M. Laurent. The author's famous result in 1996 on the algebraic independence of the values of the Ramanujan functions is the main theme of the reminder of the book. After deriving several beautiful consequences of his result, the author develops the algebraic material necessary for the proof. The two important technical tools in the proof are Philippon's criterion for algebraic independence and zero bound for Ramanujan functions. The proofs of these are covered in detail. The author also presents a direct method, without using any criterion for algebraic independence as that of Philippon, by which one can obtain lower bounds for transcendence degree of finitely generated field $\mathbb Q(\omega_1,\ldots,\omega_m)$. This is a contribution towards Schanuel's conjecture. The book is self-contained and the proofs are clear and lucid. A brief history of the topics is also given. Some sections intersect with Chapters 3 and 10 of Introduction to Algebraic Independence Theory, Lecture Notes in Mathematics, Springer, 1752, edited by Yu. V. Nesterenko and P. Philippon.

Download or read book Number Theory Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-20 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of Serge Lang’s vast contribution to mathematics, this memorial volume presents articles by prominent mathematicians. Reflecting the breadth of Lang's own interests and accomplishments, these essays span the field of Number Theory, Analysis and Geometry.

Download or read book The Transcendence and Algebraic Independence of the Values of Certain E functions written by Keijo Väänänen and published by . This book was released on 1973 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transcendental and Algebraic Numbers written by Aleksandr Osipovich Gelʹfond and published by . This book was released on 1960 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: