Download or read book Mahler s Problem in Metric Number Theory written by Vladimir Gennadievich Sprindzhuk and published by Amer Mathematical Society. This book was released on 1969 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the solutions of a group of questions related both to the general theory of transcendental numbers and to the metrical theory of diophantine (and also algebraic) approximations. The fundamental problem in this field has been known in the literature since 1932 as Mahler's conjecture. The main result of this book is a proof of Mahler's conjecture and some analogous theorems. In Part I, the Classical case of Mahler's conjecture, dealing with real and complex numbers, is considered. This part should be comprehensible to any who knows the elements of measure theory and possesses sufficient perseverance in over-coming purely logical difficulties. Part II is concerned with locally compact fields with nonarchimedean valuation. This part requires a general familiarity with the structure of fields with nonarchimedean valuation. All the necessary information is given in the text with references to the sources.
Download or read book Mahler s Problem in Metric Number Theory written by V. G. Sprindzuk and published by . This book was released on 2011-03-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the solutions of a group of questions related both to the general theory of transcendental numbers and to the metrical theory of diophantine (and also algebraic) approximations. The fundamental problem in this field has been known in the literature since 1932 as Mahler's conjecture. The main result of this book is a proof of Mahler's conjecture and some analogous theorems. In Part I, the "Classical" case of Mahler's conjecture, dealing with real and complex numbers, is considered. This part should be comprehensible to any who knows the elements of measure theory and possesses sufficient perseverance in over-coming purely logical difficulties. Part II is concerned with locally compact fields with nonarchimedean valuation. This part requires a general familiarity with the structure of fields with nonarchimedean valuation. All the necessary information is given in the text with references to the sources.
Download or read book Mahler s Problem in Metric Number Theory written by Vladimir Gennadievič Sprindžuk and published by . This book was released on 1969 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 Metric Diophantine Approximation on Manifolds written by V. I. Bernik and published by Cambridge University Press. This book was released on 1999-10-14 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. All researchers with an interest in Diophantine approximation will welcome this book.
Download or read book Many Variations of Mahler Measures written by François Brunault and published by Cambridge University Press. This book was released on 2020-05-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne–Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.
Download or read book Arnold s Problems written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2004-06-24 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
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 Metric Theory of Diophantine Approximations written by Vladimir Gennadievich Sprindzhuk and published by . This book was released on 1979 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a systematic presentation of a branch of number theory known as the metric theory of Diophantine approximation. The main emphasis is on extremal problems, i.e., problems involving approximations that are best in a certain sense.
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 Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
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.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 80 Years of Zentralblatt MATH written by Olaf Teschke and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Founded in 1931 by Otto Neugebauer as the printed documentation service “Zentralblatt für Mathematik und ihre Grenzgebiete”, Zentralblatt MATH (ZBMATH) celebrates its 80th anniversary in 2011. Today it is the most comprehensive and active reference database in pure and applied mathematics worldwide. Many prominent mathematicians have been involved in this service as reviewers or editors and have, like all mathematicians, left their footprints in ZBMATH, in a long list of entries describing all of their research publications in mathematics. This book provides one review from each of the 80 years of ZBMATH. Names like Courant, Kolmogorov, Hardy, Hirzebruch, Faltings and many others can be found here. In addition to the original reviews, the book offers the authors' profiles indicating their co-authors, their favorite journals and the time span of their publication activities. In addition to this, a generously illustrated essay by Silke Göbel describes the history of ZBMATH.
Download or read book Singularities of Caustics and Wave Fronts written by Vladimir Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
