Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6, Robert C. Gunning

Автор: Monastyrsky Michael I.
Название: Riemann, topology, and physics
ISBN: 0817647783 ISBN-13(EAN): 9780817647780
Издательство: Springer
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Цена: 55430.00 T
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Описание: The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics.

Автор: Riemann
Название: Bernard Riemann`s gesammelte mathematische Werke und wissenschaftlicher Nachlass
ISBN: 110805935X ISBN-13(EAN): 9781108059350
Издательство: Cambridge Academ
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Цена: 48570.00 T
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Описание: The collected works, in German, of the groundbreaking mathematician Bernhard Riemann (1826-66) first appeared in 1876. Included here is his famous 1854 lecture `On the hypotheses which underlie geometry`, which set in motion studies which culminated in Einstein`s general theory of relativity.

Автор: Paraskevas Alvanos
Название: Riemann-Roch Spaces and Computation
ISBN: 3110426137 ISBN-13(EAN): 9783110426137
Издательство: Walter de Gruyter
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Цена: 49530.00 T
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Описание: The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important, a variety of examples with codes of algorithms are given in the book, covering the majority of the cases.

Автор: Frankenhuijsen
Название: The Riemann Hypothesis for Function Fields
ISBN: 1107047218 ISBN-13(EAN): 9781107047211
Издательство: Cambridge Academ
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Цена: 111930.00 T
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Описание: A description of how non-commutative geometry could provide a means to attack the Riemann Hypothesis, one of the most important unsolved problems in mathematics. The book will be of interest to graduate students in analytic and algebraic number theory, and provides a strong foundation for further research in this area.

Автор: Ketcheson, David I. Leveque, Randall J. Razo, Mauricio J. Del
Название: Riemann problems and jupyter solutions
ISBN: 1611976200 ISBN-13(EAN): 9781611976205
Издательство: Mare Nostrum (Eurospan)
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Цена: 51410.00 T
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Описание: This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity.It covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem.The emphasis is on the general ideas, but each chapter delves into a particular application. The book is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations.

Автор: Frankenhuijsen
Название: The Riemann Hypothesis for Function Fields
ISBN: 1107685311 ISBN-13(EAN): 9781107685314
Издательство: Cambridge Academ
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Цена: 40130.00 T
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Описание: A description of how non-commutative geometry could provide a means to attack the Riemann Hypothesis, one of the most important unsolved problems in mathematics. The book will be of interest to graduate students in analytic and algebraic number theory, and provides a strong foundation for further research in this area.

Автор: Vasile Brinzanescu
Название: Holomorphic Vector Bundles over Compact Complex Surfaces
ISBN: 3540610189 ISBN-13(EAN): 9783540610182
Издательство: Springer
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Цена: 32600.00 T
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Описание: This text discusses the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. It also considers irreducible vector bundles and stability with respect to a Gauduchon metric.

Автор: Gunning Robert C.
Название: Lectures on Riemann Surfaces: Jacobi Varieties
ISBN: 0691646163 ISBN-13(EAN): 9780691646169
Издательство: Wiley
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Цена: 97530.00 T
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Описание: A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis pres

Автор: Bruce Gilligan; Otto Forster
Название: Lectures on Riemann Surfaces
ISBN: 1461259630 ISBN-13(EAN): 9781461259633
Издательство: Springer
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Цена: 62380.00 T
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Описание: This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations. The second chapter is devoted to compact Riemann surfaces. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle. The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy- Riemann equations and on Schwarz' Lemma.

Автор: Bost Jean-Benoоt
Название: Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles Over Arithmetic Curves
ISBN: 3030443280 ISBN-13(EAN): 9783030443283
Издательство: Springer
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Цена: 121110.00 T
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Описание: This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves.

Автор: Bobenko
Название: Computational Approach to Riemann Surfaces
ISBN: 3642174124 ISBN-13(EAN): 9783642174124
Издательство: Springer
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Цена: 41880.00 T
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Описание: 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.

Автор: Robert D.M. Accola
Название: Topics in the Theory of Riemann Surfaces
ISBN: 3540587217 ISBN-13(EAN): 9783540587217
Издательство: Springer
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Цена: 23250.00 T
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Описание: 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.