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Book Synopsis Theta Functions on Riemann Surfaces by : J. D. Fay
Download or read book Theta Functions on Riemann Surfaces written by J. D. Fay and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
Book Synopsis Elliptic Functions, Theta Functions, and Riemann Surfaces by : Harry Ernest Rauch
Download or read book Elliptic Functions, Theta Functions, and Riemann Surfaces written by Harry Ernest Rauch and published by . This book was released on 1973-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Functions, Theta Functions, and Riemann Surfaces [By] Harry E. Rauch [And] Aaron Lebowitz by : Harry Ernest Rauch
Download or read book Elliptic Functions, Theta Functions, and Riemann Surfaces [By] Harry E. Rauch [And] Aaron Lebowitz written by Harry Ernest Rauch and published by . This book was released on 1973 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Theory of Elliptic Functions by : Harris Hancock
Download or read book Lectures on the Theory of Elliptic Functions written by Harris Hancock and published by . This book was released on 1910 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theta Constants, Riemann Surfaces and the Modular Group by : Hershel M. Farkas
Download or read book Theta Constants, Riemann Surfaces and the Modular Group written by Hershel M. Farkas and published by American Mathematical Soc.. This book was released on 2001 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theta Functions with Applications to Riemann Surfaces by : Harry Ernest Rauch
Download or read book Theta Functions with Applications to Riemann Surfaces written by Harry Ernest Rauch and published by . This book was released on 1974 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Functions and Elliptic Curves by : Patrick Du Val
Download or read book Elliptic Functions and Elliptic Curves written by Patrick Du Val and published by Cambridge University Press. This book was released on 1973-08-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.
Download or read book Elliptic Curves written by Henry McKean and published by Cambridge University Press. This book was released on 1999-08-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.
Book Synopsis Tata Lectures on Theta II by : David Mumford
Download or read book Tata Lectures on Theta II written by David Mumford and published by Springer Science & Business Media. This book was released on 2012-04-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. It presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others.
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.
Book Synopsis Elliptic Integrals and Elliptic Functions by : Takashi Takebe
Download or read book Elliptic Integrals and Elliptic Functions written by Takashi Takebe and published by Springer Nature. This book was released on 2023-07-10 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader’s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book. For each notion a clear motivation is given for its study, answering the question ‘Why do we consider such objects?’, and the theory is developed in a natural way that mirrors its historical development (e.g., ‘If there is such and such an object, then you would surely expect this one’). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.
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.
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.
Book Synopsis Abel's Theorem and the Allied Theory by : Henry Frederick Baker
Download or read book Abel's Theorem and the Allied Theory written by Henry Frederick Baker and published by . This book was released on 1897 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Book Synopsis A Treatise on the Theory of Functions by : James Harkness
Download or read book A Treatise on the Theory of Functions written by James Harkness and published by . This book was released on 1893 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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