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 Рейтинг: Цена: 8554.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Eie Minking Название: Theory of Multiple Zeta Values with Applications in Combinat ISBN: 9814472638 ISBN-13(EAN): 9789814472630 Издательство: World Scientific Publishing Цена: 12989.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.
Автор: Coates Название: The Bloch–Kato Conjecture for the Riemann Zeta Function ISBN: 1107492963 ISBN-13(EAN): 9781107492967 Издательство: Cambridge Academ Рейтинг: Цена: 9029.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An account of a significant body of recent work that resolves some long-standing mysteries concerning special values of the Riemann zeta function. It brings together many important results from K-theory, motivic cohomology, and Iwasawa theory, accessible at graduate level and above.
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