Series Associated with the Zeta and Related Functions, Hari M. Srivastava; Junesang Choi
Автор: Sergey D. Odintsov; Diego S?ez-G?mez; Prof. Dr. S. Название: Cosmology, Quantum Vacuum and Zeta Functions ISBN: 3642268439 ISBN-13(EAN): 9783642268434 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.
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: 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.
Автор: Tsuneo Arakawa; Tomoyoshi Ibukiyama; Masanobu Kane Название: Bernoulli Numbers and Zeta Functions ISBN: 4431563830 ISBN-13(EAN): 9784431563839 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Andr? Voros Название: Zeta Functions over Zeros of Zeta Functions ISBN: 3642052029 ISBN-13(EAN): 9783642052026 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In the Riemann zeta function ?(s), the non-real zeros or Riemann zeros, denoted ?, play an essential role mainly in number theory, and thereby g- erate considerable interest. However, they are very elusive objects. Thus, no individual zero has an analytically known location; and the Riemann - pothesis, which states that all those zeros should lie on the critical line, i.e., 1 haverealpart, haschallengedmathematicianssince1859(exactly150years 2 ago). For analogous symmetric sets of numbers{v}, such as the roots of a k polynomial, the eigenvalues of a ?nite or in?nite matrix, etc., it is well known that symmetric functions of the{v} tend to have more accessible properties k than the individual elements v . And, we ?nd the largest wealth of explicit k properties to occur in the (generalized) zeta functions of the generic form 's Zeta(s, a)= (v +a) k k (with the extra option of replacing v here by selected functions f(v )). k k Not surprisingly, then, zeta functions over the Riemann zeros have been considered, some as early as 1917.What is surprising is how small the lite- ture on those zeta functions has remained overall.We were able to spot them in barely a dozen research articles over the whole twentieth century and in none ofthebooks featuring the Riemannzeta function. So the domainexists, but it has remained largely con?dential and sporadically covered, in spite of a recent surge of interest. Could it then be that those zeta functions have few or uninteresting pr- erties?Inactualfact, theirstudyyieldsanabundanceofquiteexplicitresults.
Автор: Andreas Juhl Название: Cohomological Theory of Dynamical Zeta Functions ISBN: 3034895240 ISBN-13(EAN): 9783034895248 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo- cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions.
Автор: Sautoy, Marcus Du Woodward, Luke Название: Zeta functions of groups and rings ISBN: 354074701X ISBN-13(EAN): 9783540747017 Издательство: Springer Рейтинг: Цена: 6282.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Zeta functions have been a powerful tool in mathematics. This book considers a fresh class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. It explores the analytic behaviour of these functions together with an investigation of functional equations.
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.
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: 25155.00 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: Roger Godement; Herve Jacquet Название: Zeta Functions of Simple Algebras ISBN: 3540057978 ISBN-13(EAN): 9783540057970 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Neal Koblitz Название: p-adic Numbers, p-adic Analysis, and Zeta-Functions ISBN: 1461270146 ISBN-13(EAN): 9781461270140 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-function, plus new exercises and an appendix of answers and hints.
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