Автор: Takashi Aoki; Shigeru Kanemitsu; Mikio Nakahara; Y Название: Zeta Functions, Topology and Quantum Physics ISBN: 1441937641 ISBN-13(EAN): 9781441937643 Издательство: Springer Рейтинг: Цена: 21953.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003.
Автор: Michel L. Lapidus; Machiel van Frankenhuijsen Название: Fractal Geometry, Complex Dimensions and Zeta Functions ISBN: 1489988386 ISBN-13(EAN): 9781489988386 Издательство: Springer Рейтинг: Цена: 10976.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.
Автор: Hugh Montgomery; Ashkan Nikeghbali; Michael Th. Ra Название: Exploring the Riemann Zeta Function ISBN: 3319599682 ISBN-13(EAN): 9783319599687 Издательство: Springer Рейтинг: Цена: 13415.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.
The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Cryptography, Mathematical Physics, and Engineering.
Автор: Markus Szymon Fraczek Название: Selberg Zeta Functions and Transfer Operators ISBN: 3319512943 ISBN-13(EAN): 9783319512945 Издательство: Springer Рейтинг: Цена: 7927.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Introduction.-Preliminaries.-The Gamma function and the incomplete Gamma functions.-The Hurwitz Zeta Function and the Lerch Zeta Function.-Computation of the spectra and eigenvectors of large complex matrices.-The hyperbolic Laplace-Beltrami operator.-Transfer operators for the geodesic flow on hyperbolic surfaces.-Numerical results for spectra and traces of the transfer operator for character deformations.-Investigations of Selberg zeta functions under character deformations.-Concluding remarks.-Appendices.-References.-Index of Notations.
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: 15855.00 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.
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.
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