Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion, Alexander Felshtyn

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: Motohashi
Название: Spectral Theory of the Riemann Zeta-Function
ISBN: 0521058074 ISBN-13(EAN): 9780521058070
Издательство: Cambridge Academ
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Цена: 57030.00 T
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Описание: Professor Motohashi shows that the Riemann zeta function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the function itself.

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;