Selberg Zeta Functions and Transfer Operators, Markus Szymon Fraczek
Автор: Neal Koblitz Название: p-adic Numbers, p-adic Analysis, and Zeta-Functions ISBN: 0387960171 ISBN-13(EAN): 9780387960173 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level.
Описание: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
Описание: Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function.
Автор: U. Christian Название: Selberg`s Zeta-, L-, and Eisensteinseries ISBN: 3540127011 ISBN-13(EAN): 9783540127017 Издательство: Springer Рейтинг: Цена: 3492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Salahoddin Shokranian Название: The Selberg-Arthur Trace Formula ISBN: 3540550216 ISBN-13(EAN): 9783540550211 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book based on lectures given by James Arthur discussesthe trace formula of Selberg and Arthur. The emphasis islaid on Arthur`s trace formula for GL(r), with severalexamples in order to illustrate the basic concepts. Orbital integrals andSelberg`s trace formula, 2.3.Three examples, 2.4.
Автор: Grosche Christian Название: Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae ISBN: 9814460079 ISBN-13(EAN): 9789814460071 Издательство: World Scientific Publishing Рейтинг: Цена: 19800.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition.In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.
Автор: Dennis A. Hejhal Название: The Selberg Trace Formula for PSL (2,R) ISBN: 3540079882 ISBN-13(EAN): 9783540079880 Издательство: Springer Рейтинг: Цена: 3766.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: A. Good Название: Local Analysis of Selberg`s Trace Formula ISBN: 3540127135 ISBN-13(EAN): 9783540127130 Издательство: Springer Рейтинг: Цена: 3492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Michel L. Lapidus; Goran Radunovi?; Darko ?ubrini? Название: Fractal Zeta Functions and Fractal Drums ISBN: 3319447041 ISBN-13(EAN): 9783319447049 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.
This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.
The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter.
Автор: J?rgen Sander; J?rn Steuding; Rasa Steuding Название: From Arithmetic to Zeta-Functions ISBN: 3319282026 ISBN-13(EAN): 9783319282022 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany.
Автор: Srivastava, H. M. Название: Zeta and q-Zeta Functions and Associated Series and Integrals ISBN: 0323165265 ISBN-13(EAN): 9780323165266 Издательство: Elsevier Science Рейтинг: Цена: 18275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals.
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