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Logarithmic Forms And Diophantine Geometry
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Book Synopsis Logarithmic Forms and Diophantine Geometry by : A. Baker
Download or read book Logarithmic Forms and Diophantine Geometry written by A. Baker and published by Cambridge University Press. This book was released on 2008-01-17 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
Book Synopsis Le Bouquet fané, ou Le titre réduit a sa valeur by :
Download or read book Le Bouquet fané, ou Le titre réduit a sa valeur written by and published by . This book was released on 179? with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diophantine Geometry by : Umberto Zannier
Download or read book Diophantine Geometry written by Umberto Zannier and published by Springer. This book was released on 2007-06-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, between April and July 2005. The authors are eminent experts in the field and present several subfields of the main topic. The volume provides a broad overview of recent research developments.
Book Synopsis Diophantine Approximations and Diophantine Equations by : Wolfgang M. Schmidt
Download or read book Diophantine Approximations and Diophantine Equations written by Wolfgang M. Schmidt and published by Springer. This book was released on 2006-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Book Synopsis Linear Forms in Logarithms and Applications by : Yann Bugeaud
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.
Book Synopsis Diophantine Triples and Linear Forms in Logarithms by : Simon Earp-Lynch
Download or read book Diophantine Triples and Linear Forms in Logarithms written by Simon Earp-Lynch and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the thesis for my master's degree in mathematics which I undertook with Dr. Omar Kihel. Over the last couple of years I have studied number theory with the aim being to develop a broader understanding of the theory of Diophantine equations and their (at times) elusive solutions. I begin my thesis by establishing some of the preliminary results while touching on their place within the history of number theory. This section finishes with an account of Alan Baker's work on linear forms in logarithms and some of its applications, after which the two theorems on Diophantine triples that this paper will aim to prove are stated. In the second section, I list a series of definitions and results of which the reader must be aware, but which I could not fit into the first section due to its historical slant. Following this, I prove a lemma on Pellian equations which generalizes the first lemma of [1]. This requires that a mistake from the proof of that lemma be fixed. Since this lemma was used in [2], this section serves to buttress that result as well. In the next two sections, I prove the two main theorems using results on linear forms in logarithms of algebraic numbers, extending the main result in [2] to $D(9)$ and $D(64)$ triples. The thesis ends with a few words on potential generalization and improvement of the main results, as well as other potential avenues of inquiry, and draws attention to some potential difficulties. The main results closely follow a paper co-written with my brother, Benjamin Earp-Lynch.
Book Synopsis Linear Forms in the Logarithms of Three Or Four Algebraic Numbers with an Application to Solving Diophantine Equations by : Lisa K. Elderbrock
Download or read book Linear Forms in the Logarithms of Three Or Four Algebraic Numbers with an Application to Solving Diophantine Equations written by Lisa K. Elderbrock and published by . This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heights in Diophantine Geometry by : Enrico Bombieri
Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by Cambridge University Press. This book was released on 2006 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
Book Synopsis Diophantine Analysis by : Jörn Steuding
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 239 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.
Book Synopsis Nevanlinna Theory and Its Relation to Diophantine Approximation by : Min Ru
Download or read book Nevanlinna Theory and Its Relation to Diophantine Approximation written by Min Ru and published by World Scientific. This book was released on 2001 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects. Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems. Contents: Nevanlinna Theory for Meromorphic Functions and Roth's Theorem; Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings; Holomorphic Curves in Pn(C) and Schmidt's Sub-Space Theorem; The Moving Target Problems; Equi-Dimensional Nevanlinna Theory and Vojta's Conjecture; Holomorphic Curves in Abelian Varieties and the Theorem of Faltings; Complex Hyperbolic Manifolds and Lang's Conjecture. Readership: Researchers in complex analysis, number theory and complex geometry.
Book Synopsis Diophantine Approximation on Linear Algebraic Groups by : Michel Waldschmidt
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.
Book Synopsis Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms by : Wai Kiu Chan
Download or read book Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms written by Wai Kiu Chan and published by American Mathematical Soc.. This book was released on 2013 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. The articles cover the arithmetic theory of quadratic forms and lattices, as well as the effective Diophantine analysis with height functions.
Book Synopsis Arithmetic Geometry, Number Theory, and Computation by : Jennifer S. Balakrishnan
Download or read book Arithmetic Geometry, Number Theory, and Computation written by Jennifer S. Balakrishnan and published by Springer Nature. This book was released on 2022-03-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Book Synopsis Introduction to Algebraic Independence Theory by : Patrice Philippon
Download or read book Introduction to Algebraic Independence Theory written by Patrice Philippon and published by Springer Science & Business Media. This book was released on 2001-01-18 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.
Book Synopsis A Panorama of Number Theory Or The View from Baker's Garden by : Gisbert Wüstholz
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.
Book Synopsis Unit Equations in Diophantine Number Theory by : Jan-Hendrik Evertse
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.
Book Synopsis Transcendental Number Theory by : Alan Baker
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.
