Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values, Zhao Jianqiang

Автор: Lapidus Michel L., Frankenhuijsen Machiel van
Название: Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings
ISBN: 0387332855 ISBN-13(EAN): 9780387332857
Издательство: Springer
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Цена: 49330.00 T
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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.

Автор: Michel L. Lapidus; Goran Radunovi?; Darko ?ubrini?
Название: Fractal Zeta Functions and Fractal Drums
ISBN: 3319447041 ISBN-13(EAN): 9783319447049
Издательство: Springer
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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.

Автор: Arakawa Tsuneo
Название: Bernoulli Numbers and Zeta Functions
ISBN: 4431549188 ISBN-13(EAN): 9784431549185
Издательство: Springer
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Цена: 102480.00 T
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Описание: The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. a formula for Bernoulli numbers by Stirling numbers; congruences between some class numbers and Bernoulli numbers;

Автор: Alexander Felshtyn
Название: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
ISBN: 0821820907 ISBN-13(EAN): 9780821820902
Издательство: Oxford Academ
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Цена: 59670.00 T
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Описание: In the paper we study dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analogue of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zefunctions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory, quantum field theory and dynamical systems.