The Riemann Zeta Function
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Exploring The Riemann Zeta Function
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Author : Hugh Montgomery
language : en
Publisher: Springer
Release Date : 2017-09-11
Exploring The Riemann Zeta Function written by Hugh Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
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.
Riemann S Zeta Function
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Author : Harold M. Edwards
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Riemann S Zeta Function written by Harold M. Edwards and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
Lectures On The Riemann Zeta Function
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Author : H. Iwaniec
language : en
Publisher: American Mathematical Society
Release Date : 2014-10-07
Lectures On The Riemann Zeta Function written by H. Iwaniec and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Mathematics categories.
The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. There are also technical lemmas which can be useful in a broader context.
The Riemann Zeta Function
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Author : Anatoly A. Karatsuba
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-03
The Riemann Zeta Function written by Anatoly A. Karatsuba and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-03 with Mathematics categories.
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The Theory Of The Riemann Zeta Function
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Author : Edward Charles Titchmarsh
language : en
Publisher: Oxford University Press
Release Date : 1986
The Theory Of The Riemann Zeta Function written by Edward Charles Titchmarsh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
The Theory Of Functions
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Author : E. C. Titchmarsh
language : en
Publisher:
Release Date : 1964
The Theory Of Functions written by E. C. Titchmarsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Calculus categories.
The Riemann Zeta Function
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Author : Anatoliĭ Alekseevich Karat︠s︡uba
language : en
Publisher: Walter de Gruyter
Release Date : 1992
The Riemann Zeta Function written by Anatoliĭ Alekseevich Karat︠s︡uba and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, 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 interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
The Bloch Kato Conjecture For The Riemann Zeta Function
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Author : John Coates
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-13
The Bloch Kato Conjecture For The Riemann Zeta Function written by John Coates and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-13 with Mathematics categories.
A graduate-level account of an important recent result concerning the Riemann zeta function.
Spectral Theory Of The Riemann Zeta Function
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Author : Yoichi Motohashi
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-11
Spectral Theory Of The Riemann Zeta Function written by Yoichi Motohashi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-11 with Mathematics categories.
The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the 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 zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function
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Author : Samuel W. Gilbert
language : en
Publisher: Riemann hypothesis
Release Date : 2009
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function written by Samuel W. Gilbert and has been published by Riemann hypothesis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.