Lecture Notes On Diophantine Analysis
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Lecture Notes On Diophantine Analysis
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Author : Umberto Zannier
language : en
Publisher: Springer
Release Date : 2015-05-05
Lecture Notes On Diophantine Analysis written by Umberto Zannier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-05 with Mathematics categories.
These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Diophantine Analysis
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Author : Jörn Steuding
language : en
Publisher: Birkhäuser
Release Date : 2016-12-21
Diophantine Analysis written by Jörn Steuding and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-21 with Mathematics categories.
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.
Diophantine Analysis
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Author : Australian Mathematical Society
language : en
Publisher:
Release Date : 2014-05-14
Diophantine Analysis written by Australian Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
These papers were presented at the 1985 Australian Mathematical Society convention. They survey recent work in Diophantine analysis.
Diophantine Analysis
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Author : Australian Mathematical Society
language : en
Publisher:
Release Date : 2013-11-09
Diophantine Analysis written by Australian Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with categories.
These papers were presented at the 1985 Australian Mathematical Society convention. They survey recent work in Diophantine analysis.
Diophantine Approximations And Diophantine Equations
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Author : Wolfgang M. Schmidt
language : en
Publisher: Springer
Release Date : 2006-12-08
Diophantine Approximations And Diophantine Equations written by Wolfgang M. Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
"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
Exploring The Number Jungle A Journey Into Diophantine Analysis
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Author : Edward B. Burger
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Exploring The Number Jungle A Journey Into Diophantine Analysis written by Edward B. Burger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--BOOK JACKET.
Integral Points On Algebraic Varieties
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Author : Pietro Corvaja
language : en
Publisher: Springer
Release Date : 2016-11-23
Integral Points On Algebraic Varieties written by Pietro Corvaja and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Mathematics categories.
This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.
Diophantine Approximation
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Author : W.M. Schmidt
language : en
Publisher: Springer
Release Date : 2009-02-05
Diophantine Approximation written by W.M. Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-05 with Mathematics categories.
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Algebraic Number Theory And Diophantine Analysis
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Author : Franz Halter-Koch
language : en
Publisher: Walter de Gruyter
Release Date : 2000
Algebraic Number Theory And Diophantine Analysis written by Franz Halter-Koch and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
No detailed description available for "Algebraic Number Theory and Diophantine Analysis".
Class Groups Of Number Fields And Related Topics
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Author : Kalyan Chakraborty
language : en
Publisher: Springer Nature
Release Date : 2020-01-17
Class Groups Of Number Fields And Related Topics written by Kalyan Chakraborty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-17 with Mathematics categories.
This book gathers original research papers and survey articles presented at the “International Conference on Class Groups of Number Fields and Related Topics,” held at Harish-Chandra Research Institute, Allahabad, India, on September 4–7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer–Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.