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Metric Diophantine Approximation On Manifolds
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Book Synopsis Metric Diophantine Approximation on Manifolds by : V. I. Bernik
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.
Book Synopsis Metric Theory of Diophantine Approximations by : Vladimir Gennadievich Sprindzhuk
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.
Book Synopsis Dynamics, Geometry, Number Theory by : David Fisher
Download or read book Dynamics, Geometry, Number Theory written by David Fisher and published by University of Chicago Press. This book was released on 2022-02-07 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--
Book Synopsis Number Theory Meets Wireless Communications by : Victor Beresnevich
Download or read book Number Theory Meets Wireless Communications written by Victor Beresnevich and published by Springer Nature. This book was released on 2021-01-08 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this volume stem from the Workshop on Interactions between Number Theory and Wireless Communication held at the University of York in 2016. The chapters, written by leading experts in their respective fields, provide direct overviews of highly exciting current research developments. The topics discussed include metric Diophantine approximation, geometry of numbers, homogeneous dynamics, algebraic lattices and codes, network and channel coding, and interference alignment. The book is edited by experts working in number theory and communication theory. It thus provides unique insight into key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research. Great effort has been made to present the material in a manner that is accessible to new researchers, including PhD students. The book will also be essential reading for established researchers working in number theory or wireless communications looking to broaden their outlook and contribute to this emerging interdisciplinary area.
Book Synopsis Limit Theorems in Probability, Statistics and Number Theory by : Peter Eichelsbacher
Download or read book Limit Theorems in Probability, Statistics and Number Theory written by Peter Eichelsbacher and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.
Book Synopsis Dynamics and Analytic Number Theory by : Dzmitry Badziahin
Download or read book Dynamics and Analytic Number Theory written by Dzmitry Badziahin and published by Cambridge University Press. This book was released on 2016-11-10 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.
Book Synopsis Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces by : Lior Fishman
Download or read book Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces written by Lior Fishman and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic 1976 paper to more recent results of Hersonsky and Paulin (2002, 2004, 2007). The authors consider concrete examples of situations which have not been considered before. These include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which the authors are aware, the results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones (1997) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson–Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem.
Book Synopsis Dynamics: Topology and Numbers by : Pieter Moree
Download or read book Dynamics: Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich and published by American Mathematical Soc.. This book was released on 2006 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\p$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarník concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantineapproximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarník's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarník's theorem opens up the Duffin-Schaeffer conjecturefor Hausdorff measures.
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich Detta Dickinson Sanju Velani
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich Detta Dickinson Sanju Velani and published by American Mathematical Soc.. This book was released on 2005-12-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\psi$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.
Book Synopsis Horizons of Fractal Geometry and Complex Dimensions by : Robert G. Niemeyer
Download or read book Horizons of Fractal Geometry and Complex Dimensions written by Robert G. Niemeyer and published by American Mathematical Soc.. This book was released on 2019-06-26 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
Book Synopsis Recent Trends in Ergodic Theory and Dynamical Systems by : Siddhartha Bhattacharya
Download or read book Recent Trends in Ergodic Theory and Dynamical Systems written by Siddhartha Bhattacharya and published by American Mathematical Soc.. This book was released on 2015-01-26 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Recent Trends in Ergodic Theory and Dynamical Systems, in honor of S. G. Dani's 65th Birthday, held December 26-29, 2012, in Vadodara, India. This volume covers many topics of ergodic theory, dynamical systems, number theory and probability measures on groups. Included are papers on Teichmüller dynamics, Diophantine approximation, iterated function systems, random walks and algebraic dynamical systems, as well as two surveys on the work of S. G. Dani.
Book Synopsis Approximation Results in Topological Manifolds by : Thomas A. Chapman
Download or read book Approximation Results in Topological Manifolds written by Thomas A. Chapman and published by American Mathematical Soc.. This book was released on 1981 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of results are established concerning the approximation of maps between topological manifolds by homeomorphisms, approximate fibrations, and block bundles. Applications are given to the approximation of approximate fibrations by block bundles, and to the taming of locally homotopically unknotted embeddings.
Book Synopsis Littlewood and Duffin–Schaeffer-Type Problems in Diophantine Approximation by : Sam Chow
Download or read book Littlewood and Duffin–Schaeffer-Type Problems in Diophantine Approximation written by Sam Chow and published by American Mathematical Society. This book was released on 2024-05-15 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Dynamics and Analytic Number Theory by : Dzmitry Badziahin
Download or read book Dynamics and Analytic Number Theory written by Dzmitry Badziahin and published by Cambridge University Press. This book was released on 2016-11-10 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Book Synopsis Approximation by Algebraic Numbers by : Yann Bugeaud
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.
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 2001-06-06 with total page 338 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.
