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Contributions To The Theory Of Zeta Functions
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Book Synopsis Contributions To The Theory Of Zeta-functions: The Modular Relation Supremacy by : Shigeru Kanemitsu
Download or read book Contributions To The Theory Of Zeta-functions: The Modular Relation Supremacy written by Shigeru Kanemitsu and published by World Scientific. This book was released on 2014-12-15 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a systematic survey of almost all the equivalent assertions to the functional equations — zeta symmetry — which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions.This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Book Synopsis Contributions to the Theory of Zeta-Functions by : Shigeru Kanemitsu
Download or read book Contributions to the Theory of Zeta-Functions written by Shigeru Kanemitsu and published by World Scientific. This book was released on 2014-12-15 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Book Synopsis Contributions to the Theory of the Riemann Zeta-function by : Atle Selberg
Download or read book Contributions to the Theory of the Riemann Zeta-function written by Atle Selberg and published by . This book was released on 1946 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Contributions to the Theory of the Riemann Zeta-function and the Theory of the Distribution of Primes by : Godfrey Harold Hardy
Download or read book Contributions to the Theory of the Riemann Zeta-function and the Theory of the Distribution of Primes written by Godfrey Harold Hardy and published by . This book was released on 1982 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ten Physical Applications of Spectral Zeta Functions by : Emilio Elizalde
Download or read book Ten Physical Applications of Spectral Zeta Functions written by Emilio Elizalde and published by Springer. This book was released on 2012-05-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta-function regularization is a powerful method in perturbation theory, and this book is a comprehensive guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice, for example in the Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, and non-commutative spacetime. The formulae, some of which are new, can be directly applied in creating physically meaningful, accurate numerical calculations. The book acts both as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice. Thoroughly revised, updated and expanded, this new edition includes novel, explicit formulas on the general quadratic, the Chowla-Selberg series case, an interplay with the Hadamard calculus, and also features a fresh chapter on recent cosmological applications, including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.
Book Synopsis Exploring the Riemann Zeta Function by : Hugh Montgomery
Download or read book Exploring the Riemann Zeta Function written by Hugh Montgomery and published by Springer. This book was released on 2017-09-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Mathematical Physics, Engineering and Cryptography.
Book Synopsis An Introduction to the Theory of the Riemann Zeta-Function by : S. J. Patterson
Download or read book An Introduction to the Theory of the Riemann Zeta-Function written by S. J. Patterson and published by Cambridge University Press. This book was released on 1995-02-02 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.
Book Synopsis Zeta Functions, Topology and Quantum Physics by : Takashi Aoki
Download or read book Zeta Functions, Topology and Quantum Physics written by Takashi Aoki and published by Springer Science & Business Media. This book was released on 2008-05-10 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.
Book Synopsis An Introduction to the Theory of the Riemann Zeta-Function by : S. J. Patterson
Download or read book An Introduction to the Theory of the Riemann Zeta-Function written by S. J. Patterson and published by Cambridge University Press. This book was released on 1995-02-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro
Book Synopsis Ten Physical Applications of Spectral Zeta Functions by : Emilio Elizalde
Download or read book Ten Physical Applications of Spectral Zeta Functions written by Emilio Elizalde and published by Springer Science & Business Media. This book was released on 2008-12-04 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monography is, in the first place, a commented guide that invites the reader to plunge into the thrilling world ofzeta functions and their appli cations in physics. Different aspects ofthis field ofknowledge are considered, as one can see specifically in the Table of Contents. The level of the book is elementary. It is intended for people with no or little knowledge of the subject. Everything is explained in full detail, in particular, the mathematical difficulties and tricky points, which too often constitute an insurmountable barrier for those who would have liked to be come aquainted with that matter but never dared to ask (or did not manage to understand more complete, higher-level treatises). In this sense the present work is to be considered as a basic introduction and exercise collection for other books that have appeared recently. Concerning the physical applications of the method ofzeta-function reg ularization here described, quite a big choice is presented. The reader must be warned, however, that I have not tried to explain the underlying physi cal theories in complete detail (since this is undoubtedly out of scope), but rather to illustrate - simply and clearly - the precise way the method must be applied. Sometimes zeta regularization is explicitly compared in the text with other procedures the reader is supposed to be more familiar with (such as cut-off or dimensional regularization).
Book Synopsis Contributions to the Theory of the Dirichlet L-series and the Epstein Zeta Functions by : Carl Ludwig Siegel
Download or read book Contributions to the Theory of the Dirichlet L-series and the Epstein Zeta Functions written by Carl Ludwig Siegel and published by . This book was released on 1943 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Bloch–Kato Conjecture for the Riemann Zeta Function by : John Coates
Download or read book The Bloch–Kato Conjecture for the Riemann Zeta Function written by John Coates and published by Cambridge University Press. This book was released on 2015-03-19 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
Book Synopsis An Introduction to the Theory of Local Zeta Functions by : Jun-ichi Igusa
Download or read book An Introduction to the Theory of Local Zeta Functions written by Jun-ichi Igusa and published by American Mathematical Soc.. This book was released on 2000 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba
Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Book Synopsis The Theory of the Riemann Zeta-function by : Edward Charles Titchmarsh
Download or read book The Theory of the Riemann Zeta-function written by Edward Charles Titchmarsh and published by Oxford University Press. This book was released on 1986 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.
Book Synopsis Zeta and Q-Zeta Functions and Associated Series and Integrals by : H. M. Srivastava
Download or read book Zeta and Q-Zeta Functions and Associated Series and Integrals written by H. M. Srivastava and published by Elsevier. This book was released on 2011-10-25 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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
Book Synopsis The Theory of Hardy's Z-Function by : A. Ivić
Download or read book The Theory of Hardy's Z-Function written by A. Ivić and published by Cambridge University Press. This book was released on 2013 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
