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Author : R.D.M. Accola
Publisher : Springer
Page : 109 pages
File Size : 54,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540376026
Author : Robert D. M. Accola
Publisher : Springer
Page : 105 pages
File Size : 55,5 Mb
Release : 1975-01-01
Category : Abel, Groupes d'
ISBN : 0387073981
Author : J. D. Fay
Publisher : Springer
Page : 142 pages
File Size : 42,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540378150
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.
Author : Robert C. Gunning
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642663826
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.
Author : José María Muñoz Porras,Iberoamerican Congress on Geometry,Sevín Recillas-Pishmish
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 51,7 Mb
Release : 2006
Category : Abelian groups
ISBN : 9780821838556
Most of the papers in this book deal with the theory of Riemann surfaces (moduli problems, automorphisms, etc.), abelian varieties, theta functions, and modular forms. Some of the papers contain surveys on the recent results in the topics of current interest to mathematicians, whereas others contain new research results.
Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 54,8 Mb
Release : 1972
Category : Fonctions abéliennes
ISBN : 9780821818299
Author : Harry Ernest Rauch,Hershel M. Farkas
Publisher : Unknown
Page : 258 pages
File Size : 55,6 Mb
Release : 1974
Category : Functions, Abelian
ISBN : CORNELL:31924001863814
Author : Lars Valerian Ahlfors
Publisher : Princeton University Press
Page : 436 pages
File Size : 53,5 Mb
Release : 1971-07-21
Category : Mathematics
ISBN : 069108081X
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.
Author : John David Fay
Publisher : Springer
Page : 137 pages
File Size : 40,7 Mb
Release : 1973-01-01
Category : Fonction theta
ISBN : 0387065172
Author : Robert D.M. Accola
Publisher : Springer
Page : 117 pages
File Size : 49,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540490562
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
Author : John R. Quine,Peter Sarnak
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 41,5 Mb
Release : 1997
Category : Extremal problems (Mathematics)
ISBN : 9780821805145
Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric.
Author : H. M. Farkas,I. Kra
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468499308
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.
Author : Lars Valerian Ahlfors
Publisher : Princeton University Press
Page : 432 pages
File Size : 42,5 Mb
Release : 1971-07-21
Category : Mathematics
ISBN : 9780691080819
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.
Author : L. Beshaj,T. Shaska,E. Zhupa
Publisher : IOS Press
Page : 387 pages
File Size : 53,8 Mb
Release : 2015-07-16
Category : Computers
ISBN : 9781614995203
This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
Author : Irwin Kra,Bernard Maskit
Publisher : Princeton University Press
Page : 533 pages
File Size : 40,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881550
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
