Automorphic Forms And Kleinian Groups

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Automorphic Forms And Kleinian Groups

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Author : Irwin Kra
language : en
Publisher: Addison Wesley Longman
Release Date : 1972

Automorphic Forms And Kleinian Groups written by Irwin Kra and has been published by Addison Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.

Kleinian Groups

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Author : Bernard Maskit
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Kleinian Groups written by Bernard Maskit and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations. From the point of view of uniformizations of Riemann surfaces, Bers' observation has the consequence that the question of understanding the different uniformizations of a finite Riemann surface poses a purely topological problem; it is independent of the conformal structure on the surface. The last two chapters here give a topological description of the set of all (geometrically finite) uniformizations of finite Riemann surfaces. We carefully skirt Ahlfors' finiteness theorem. For groups which uniformize a finite Riemann surface; that is, groups with an invariant component, one can either start with the assumption that the group is finitely generated, and then use the finiteness theorem to conclude that the group represents only finitely many finite Riemann surfaces, or, as we do here, one can start with the assumption that, in the invariant component, the group represents a finite Riemann surface, and then, using essentially topological techniques, reach the same conclusion. More recently, Bill Thurston wrought a revolution in the field by showing that one could analyze Kleinian groups using 3-dimensional hyperbolic geome try, and there is now an active school of research using these methods.

Automorphic Forms And Galois Representations

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Author : Fred Diamond
language : en
Publisher: Cambridge University Press
Release Date : 2014-10-16

Automorphic Forms And Galois Representations written by Fred Diamond and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Mathematics categories.

Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Discontinuous Groups And Automorphic Functions

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Author : Joseph Lehner
language : en
Publisher: American Mathematical Soc.
Release Date : 1964-12-31

Discontinuous Groups And Automorphic Functions written by Joseph Lehner 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 1964-12-31 with Mathematics categories.

Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject. The book is directed to three classes of readers: graduate students approaching the subject for the first time, mature mathematicians who wish to gain some knowledge and understanding of automorphic function theory, and experts.

Quasiconformal Mappings And Analysis

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Author : Peter Duren
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Quasiconformal Mappings And Analysis written by Peter Duren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Automorphic Forms And Related Topics

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Author : Samuele Anni
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-19

Automorphic Forms And Related Topics written by Samuele Anni 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 2019-06-19 with Mathematics categories.

This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.

Holomorphic Automorphic Forms And Cohomology

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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

Holomorphic Automorphic Forms And Cohomology written by Roelof Bruggeman 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 2018-05-29 with Mathematics categories.

Conformal Geometry Of Discrete Groups And Manifolds

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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov 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 2011-06-24 with Mathematics categories.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

The Geometry Of Discrete Groups

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Author : Alan F. Beardon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Geometry Of Discrete Groups written by Alan F. Beardon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right.

Theta Constants Riemann Surfaces And The Modular Group

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Author : Hershel M. Farkas
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Theta Constants Riemann Surfaces And The Modular Group written by Hershel M. Farkas 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 2001 with Mathematics categories.

There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for number-theoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL (2,\mathbb{Z )$, which provide another path for insights into number theory. Farkas and Kra, well-known masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for research-level problems. The text is suitable for a graduate course or for independent reading.