Описание: This book reviews higher dimensional Nevanlinna theory and its relationship with Diophantine approximation theory. Coverage builds up from the classical theory of meromorphic functions on the complex plane with full proofs, to the current state of research.
Автор: William Cherry; Zhuan Ye Название: Nevanlinna`s Theory of Value Distribution ISBN: 3642085687 ISBN-13(EAN): 9783642085680 Издательство: Springer Рейтинг: Цена: 11872.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis. On the other hand, the monograph also serves as a valuable reference for the research specialist because the authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its "number-theoretic digressions." These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.
Описание: This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations.
Following a comprehensive treatment of Nevanlinna's theory of value distribution, the author presents advances made since Hayman's work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot-Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman-Pang method of re-scaling to algebraic differential equations, and presents the Painlev -Yosida theorem, which relates Painlev transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions.
Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.
Описание: This book reviews higher dimensional Nevanlinna theory and its relationship with Diophantine approximation theory. Coverage builds up from the classical theory of meromorphic functions on the complex plane with full proofs, to the current state of research.
Автор: Olavi Nevanlinna Название: Convergence of Iterations for Linear Equations ISBN: 3764328657 ISBN-13(EAN): 9783764328658 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discussing the convergence of Krylov subspace methods for solving fixed point problems, this work focuses on the dynamical aspects of the iteration processes and outlines all the phases of a lifespan of an iteration.
Автор: Serge Lang; William Cherry Название: Topics in Nevanlinna Theory ISBN: 3540527850 ISBN-13(EAN): 9783540527855 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presents notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp. Cn.
Автор: Frithjof Nevanlinna; Phillip Emig; Phillip Emig; R Название: Absolute Analysis ISBN: 3662002515 ISBN-13(EAN): 9783662002513 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The first edition of this book, published in German, came into being as the result of lectures which the authors held over a period of several years since 1953 at the Universities of Helsinki and Zurich. The present new English edition deviates at several points from the first edition (d.
Автор: Istv?n Ga?l Название: Diophantine Equations and Power Integral Bases ISBN: 3030238644 ISBN-13(EAN): 9783030238643 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis.
Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied.
Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required.
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