Riemann Surfaces And Generalized Theta Functions

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Riemann Surfaces and Generalized Theta Functions

Author : Robert C. Gunning
Publisher : Springer Science & Business Media
ISBN 13 : 3642663826
Total Pages : 177 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Riemann Surfaces and Generalized Theta Functions by : Robert C. Gunning

Download or read book Riemann Surfaces and Generalized Theta Functions written by Robert C. Gunning and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.

Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups

Author : R.D.M. Accola
Publisher : Springer
ISBN 13 : 354037602X
Total Pages : 109 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups by : R.D.M. Accola

Download or read book Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups written by R.D.M. Accola and published by Springer. This book was released on 2006-11-14 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups

Author : Robert D. M. Accola
Publisher : Springer
ISBN 13 : 9780387073989
Total Pages : 105 pages
Book Rating : 4.0/5 (739 download)

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Book Synopsis Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups by : Robert D. M. Accola

Download or read book Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups written by Robert D. M. Accola and published by Springer. This book was released on 1975-01-01 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Riemann Surfaces

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461220343
Total Pages : 379 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Riemann Surfaces by : Hershel M. Farkas

Download or read book Riemann Surfaces written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.

Computational Approach to Riemann Surfaces

Author : Alexander I. Bobenko
Publisher : Springer Science & Business Media
ISBN 13 : 3642174124
Total Pages : 268 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Computational Approach to Riemann Surfaces by : Alexander I. Bobenko

Download or read book Computational Approach to Riemann Surfaces written by Alexander I. Bobenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Riemann Surfaces of Infinite Genus

Author : Joel S. Feldman
Publisher : American Mathematical Soc.
ISBN 13 : 082183357X
Total Pages : 306 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Riemann Surfaces of Infinite Genus by : Joel S. Feldman

Download or read book Riemann Surfaces of Infinite Genus written by Joel S. Feldman and published by American Mathematical Soc.. This book was released on 2003 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps. The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of Kadomcev-Petviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces). The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.

Probability Measures on Locally Compact Groups

Author : H. Heyer
Publisher : Springer
ISBN 13 : 9783540083320
Total Pages : 552 pages
Book Rating : 4.0/5 (833 download)

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Book Synopsis Probability Measures on Locally Compact Groups by : H. Heyer

Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer. This book was released on 1977-12-29 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Riemann Surfaces, Theta Functions, and Abelian Automorphism Groups

Author : Robert D. M. Accola
Publisher :
ISBN 13 :
Total Pages : 105 pages
Book Rating : 4.:/5 (61 download)

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Book Synopsis Riemann Surfaces, Theta Functions, and Abelian Automorphism Groups by : Robert D. M. Accola

Download or read book Riemann Surfaces, Theta Functions, and Abelian Automorphism Groups written by Robert D. M. Accola and published by . This book was released on 1975 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66

Author : Lars Valerian Ahlfors
Publisher : Princeton University Press
ISBN 13 : 1400822491
Total Pages : 433 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66 by : Lars Valerian Ahlfors

Download or read book Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66 written by Lars Valerian Ahlfors and published by Princeton University Press. This book was released on 1971-07-01 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

Riemann Surfaces

Author : H. M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1468499300
Total Pages : 348 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Riemann Surfaces by : H. M. Farkas

Download or read book Riemann Surfaces written by H. M. Farkas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the culmination often years' work separately and joint ly. The idea of writing this book began with a set of notes for a course given by one of the authors in 1970-1971 at the Hebrew University. The notes were refined serveral times and used as the basic content of courses given sub sequently by each of the authors at the State University of New York at Stony Brook and the Hebrew University. In this book we present the theory of Riemann surfaces and its many dif ferent facets. We begin from the most elementary aspects and try to bring the reader up to the frontier of present-day research. We treat both open and closed surfaces in this book, but our main emphasis is on the compact case. In fact, Chapters III, V, VI, and VII deal exclusively with compact surfaces. Chapters I and II are preparatory, and Chapter IV deals with uniformization. All works on Riemann surfaces go back to the fundamental results of Rie mann, Jacobi, Abel, Weierstrass, etc. Our book is no exception. In addition to our debt to these mathematicians of a previous era, the present work has been influenced by many contemporary mathematicians.

Advances in the Theory of Riemann Surfaces

Author : Lars Valerian Ahlfors
Publisher : Princeton University Press
ISBN 13 : 9780691080819
Total Pages : 436 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Advances in the Theory of Riemann Surfaces by : Lars Valerian Ahlfors

Download or read book Advances in the Theory of Riemann Surfaces written by Lars Valerian Ahlfors and published by Princeton University Press. This book was released on 1971-07-21 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

Compact Riemann Surfaces

Author : R. Narasimhan
Publisher : Birkhäuser
ISBN 13 : 3034886179
Total Pages : 127 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Compact Riemann Surfaces by : R. Narasimhan

Download or read book Compact Riemann Surfaces written by R. Narasimhan and published by Birkhäuser. This book was released on 2012-12-06 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Course in Complex Analysis and Riemann Surfaces

Author : Wilhelm Schlag
Publisher : American Mathematical Society
ISBN 13 : 0821898477
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag

Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

Generalized Analytic Functions on Riemann Surfaces

Author : Yuri L. Rodin
Publisher : Springer
ISBN 13 : 3540480188
Total Pages : 134 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Generalized Analytic Functions on Riemann Surfaces by : Yuri L. Rodin

Download or read book Generalized Analytic Functions on Riemann Surfaces written by Yuri L. Rodin and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Methods in Complex Analysis (AM-137), Volume 137

Author : Thomas Bloom
Publisher : Princeton University Press
ISBN 13 : 1400882575
Total Pages : 360 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Modern Methods in Complex Analysis (AM-137), Volume 137 by : Thomas Bloom

Download or read book Modern Methods in Complex Analysis (AM-137), Volume 137 written by Thomas Bloom and published by Princeton University Press. This book was released on 2016-03-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 1556080085
Total Pages : 556 pages
Book Rating : 4.5/5 (56 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1993-01-31 with total page 556 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 fme 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.

Generalizations of Thomae's Formula for Zn Curves

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 144197847X
Total Pages : 368 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Generalizations of Thomae's Formula for Zn Curves by : Hershel M. Farkas

Download or read book Generalizations of Thomae's Formula for Zn Curves written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2010-11-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. "Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory. This book is intended for mathematicians with an interest in complex analysis, algebraic geometry or number theory as well as physicists studying conformal field theory.