Theta Functions On Riemann Surfaces

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Theta Functions On Riemann Surfaces

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Author : J. D. Fay
language : en
Publisher: Springer
Release Date : 2006-11-15

Theta Functions On Riemann Surfaces written by J. D. Fay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenerate Riemann surfaces, Schottky relations for surfaces of special moduli, and theta functions on finite bordered Riemann surfaces.

Theta Functions With Applications To Riemann Surfaces

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Author : Harry Ernest Rauch
language : en
Publisher:
Release Date : 1974

Theta Functions With Applications To Riemann Surfaces written by Harry Ernest Rauch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Functions, Abelian categories.

Riemann Surfaces And Generalized Theta Functions

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Author : Robert C. Gunning
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Riemann Surfaces And Generalized Theta Functions written by Robert C. Gunning 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 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

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Author : R.D.M. Accola
language : en
Publisher: Springer
Release Date : 2006-11-14

Riemann Surfaces Theta Functions And Abelian Automorphisms Groups written by R.D.M. Accola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Theta Functions On Riemann Surfaces

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Author : John David Fay
language : en
Publisher: Springer
Release Date : 1973-01-01

Theta Functions On Riemann Surfaces written by John David Fay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Fonction theta categories.

Complex Analysis Riemann Surfaces And Integrable Systems

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Author : Sergey M. Natanzon
language : en
Publisher: Springer Nature
Release Date : 2020-01-03

Complex Analysis Riemann Surfaces And Integrable Systems written by Sergey M. Natanzon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

Compact Riemann Surfaces

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Author : R. Narasimhan
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-09-01

Compact Riemann Surfaces written by R. Narasimhan 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 1992-09-01 with Mathematics categories.

The lecture notes forming a course given by the author at the Eidgenossische Technische Hochschule, Zurich, from November 1984 to February 1985. Presents the basic theorems about the Jacobian from Riemann's own point of view. Annotation copyrighted by Book News, Inc., Portland, OR

Riemann Surfaces

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Author : H. M. Farkas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Riemann Surfaces written by H. M. Farkas 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 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.

Riemann Surfaces

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Author : Hershel M. Farkas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Riemann Surfaces written by Hershel M. Farkas 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.

It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century. It is particularly pleasing that the subject of Riemann surfaces has attracted the attention of a new generation of mathematicians from (newly) adjacent fields (for example, those interested in hyperbolic manifolds and iterations of rational maps) and young physicists who have been convinced (certainly not by mathematicians) that compact Riemann surfaces may play an important role in their (string) universe. We hope that non-mathematicians as well as mathematicians (working in nearby areas to the central topic of this book) will also learn part of this subject for the sheer beauty and elegance of the material (work of Weierstrass, Jacobi, Riemann, Hilbert, Weyl) and as healthy exposure to the way (some) mathematicians write about mathematics. We had intended a more comprehensive revision, including a fuller treatment of moduli problems and theta functions. Pressure of other commitments would have substantially delayed (by years) the appearance of the book we wanted to produce. We have chosen instead to make a few modest additions and to correct a number of errors. We are grateful to the readers who pointed out some of our mistakes in the first edition; the responsibility for the remaining mistakes carried over from the first edition and for any new ones introduced into the second edition remains with the authors. June 1991 Jerusalem H. M.

Ernst Equation And Riemann Surfaces

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Author : Christian Klein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-18

Ernst Equation And Riemann Surfaces written by Christian Klein 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 2005-11-18 with Science categories.

Exact solutions to Einstein’s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.