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 Algebraic Independence of the Values at Algebraic Points of a Class of Functions Condidered by Mahler written by N. C. Wass and published by . This book was released on 1990 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mahler Functions and Transcendence written by Kumiko Nishioka and published by Springer. This book was released on 2006-11-14 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatise of the transcendence theory of Mahler functions and their values. Recently the theory has seen profound development and has found a diversity of applications. The book assumes a background in elementary field theory, p-adic field, algebraic function field of one variable and rudiments of ring theory. The book is intended for both graduate students and researchers who are interested in transcendence theory. It will lay the foundations of the theory of Mahler functions and provide a source of further research.
Download or read book Approximation by Algebraic Numbers written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2004-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and broad account of the approximation and classification of real numbers suited for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the comprehensive list of more than 600 references.
Download or read book Number Theory written by R.P. Bambah and published by Birkhäuser. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.
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 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 A Panorama of Number Theory Or The View from Baker s Garden written by Gisbert Wüstholz and published by Cambridge University Press. This book was released on 2002-09-26 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a selection of high quality articles on number theory by leading figures.
Download or read book Journ es Arithm tiques 1980 written by J. V. Armitage and published by Cambridge University Press. This book was released on 1982-09-16 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers all branches of number theory.
Download or read book Number Theory and Analysis written by Anatoliĭ Alekseevich Karat︠s︡uba and published by American Mathematical Soc.. This book was released on 1995 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This collection consists of papers ... devoted to current trends in analytic number theory, function theory, algebraic number theory, algebraic geometry, and combinatorics" -- t.p. verso.
Download or read book A Central Limit Theorem for Processes Generated by a Family of Transformations written by Marian Jabłoński and published by . This book was released on 1991 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory IV written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On a Conjecture of Mahler Concerning the Algebraic Independence of the Values of Some E functions written by Keijo Väänänen and published by . This book was released on 1972 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theoretic Methods written by Shigeru Kanemitsu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.
Download or read book Number Theory and Its Applications in China written by Yuan Wang and published by American Mathematical Soc.. This book was released on 1988 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.
Download or read book Encyclopaedia of Mathematics Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Download or read book Number Theory and Related Fields written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2013-05-16 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.
