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Author : Yann Bugeaud
Publisher :
ISBN 13 : 9783037196830
Total Pages : pages
Book Rating : 4.1/5 (968 download)
Download or read book Linear Forms in Logarithms and Applications written by Yann Bugeaud and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 038749894X
Total Pages : 619 pages
Book Rating : 4.3/5 (874 download)
Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Author : Jörn Steuding
Publisher : Birkhäuser
ISBN 13 : 3319488171
Total Pages : 232 pages
Book Rating : 4.3/5 (194 download)
Download or read book Diophantine Analysis written by Jörn Steuding and published by Birkhäuser. This book was released on 2016-12-21 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.
Author : Saradha Natarajan
Publisher : Springer Nature
ISBN 13 : 9811541558
Total Pages : 184 pages
Book Rating : 4.8/5 (115 download)
Download or read book Pillars of Transcendental Number Theory written by Saradha Natarajan and published by Springer Nature. This book was released on 2020-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alan Baker
Publisher : Cambridge University Press
ISBN 13 : 9780521335454
Total Pages : 456 pages
Book Rating : 4.3/5 (354 download)
Download or read book New Advances in Transcendence Theory written by Alan Baker and published by Cambridge University Press. This book was released on 1988-10-13 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.
Author : Purabi Mukherji
Publisher : Springer Nature
ISBN 13 : 9811596204
Total Pages : 187 pages
Book Rating : 4.8/5 (115 download)
Download or read book Research Schools on Number Theory in India written by Purabi Mukherji and published by Springer Nature. This book was released on 2021-01-05 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar—including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.
Author : A.N. Parshin
Publisher : Springer Science & Business Media
ISBN 13 : 3662036444
Total Pages : 351 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Yann Bugeaud
Publisher :
ISBN 13 : 9783037191835
Total Pages : 0 pages
Book Rating : 4.1/5 (918 download)
Download or read book Linear Forms in Logarithms and Applications written by Yann Bugeaud and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in $p$-adic logarithms) and how this theory applies to many Diophantine problems, including the e#xB;ffective resolution of Diophantine equations, the $abc$-conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.
Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
ISBN 13 : 1009050036
Total Pages : 242 pages
Book Rating : 4.0/5 (9 download)
Download or read book Effective Results and Methods for Diophantine Equations over Finitely Generated Domains written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2022-04-28 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
Author : Jonathan M. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461466423
Total Pages : 395 pages
Book Rating : 4.4/5 (614 download)
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.
Author : Michel Waldschmidt
Publisher : Springer Science & Business Media
ISBN 13 : 3662115697
Total Pages : 649 pages
Book Rating : 4.6/5 (621 download)
Download or read book Diophantine Approximation on Linear Algebraic Groups written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Władysław Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 0857295322
Total Pages : 659 pages
Book Rating : 4.8/5 (572 download)
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Minaketan Behara
Publisher : Walter de Gruyter
ISBN 13 : 3110886723
Total Pages : 768 pages
Book Rating : 4.1/5 (18 download)
Download or read book Mathematics and Theoretical Physics written by Minaketan Behara and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author : Annette Huber
Publisher : Cambridge University Press
ISBN 13 : 1316519937
Total Pages : 265 pages
Book Rating : 4.3/5 (165 download)
Download or read book Transcendence and Linear Relations of 1-Periods written by Annette Huber and published by Cambridge University Press. This book was released on 2022-05-26 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Author : Gisbert Wüstholz
Publisher : Cambridge University Press
ISBN 13 : 9780521807999
Total Pages : 378 pages
Book Rating : 4.8/5 (79 download)
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.
Author : Pietro Corvaja
Publisher : Cambridge University Press
ISBN 13 : 1108424945
Total Pages : 209 pages
Book Rating : 4.1/5 (84 download)
Download or read book Applications of Diophantine Approximation to Integral Points and Transcendence written by Pietro Corvaja and published by Cambridge University Press. This book was released on 2018-05-03 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.
Author : Graham Everest
Publisher : American Mathematical Soc.
ISBN 13 : 1470423154
Total Pages : 318 pages
Book Rating : 4.4/5 (74 download)
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
