Exploring The Riemann Zeta Function
DOWNLOAD
Download Exploring The Riemann Zeta Function PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Exploring The Riemann Zeta Function book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Exploring The Riemann Zeta Function
DOWNLOAD
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
DOWNLOAD
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
DOWNLOAD
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.
Unraveling The Enigma Of Riemann S Zeta Function A Journey Through The Realm Of Analytic Number Theory
DOWNLOAD
Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-10
Unraveling The Enigma Of Riemann S Zeta Function A Journey Through The Realm Of Analytic Number Theory written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-10 with Mathematics categories.
In the vast expanse of mathematical inquiry, few concepts have captured the imagination and ignited the curiosity of scholars like the Riemann zeta-function. Introduced by Bernhard Riemann in the 19th century, this enigmatic function has stood as a towering enigma, challenging mathematicians and inspiring generations of exploration. This comprehensive and engaging book invites you on an intellectual journey through the captivating world of the Riemann zeta-function, unveiling its intricate properties, profound applications, and historical significance. Delve into the depths of analytic number theory as we navigate concepts like Dirichlet's theorem, the prime number theorem, and the Riemann zeta-function's relationship with other mathematical functions. Unravel the mysteries surrounding the Riemann hypothesis, a conjecture that has captivated mathematicians for over a century. Discover the profound implications of this hypothesis, its potential to unlock the secrets of prime numbers, and its role in shaping our understanding of the fundamental nature of mathematics. Witness the Riemann zeta-function's remarkable applications in diverse fields, ranging from physics and computer science to finance and engineering. Explore its contributions to quantum field theory, string theory, coding theory, and cryptography, gaining insights into the function's versatility and far-reaching impact. Trace the Riemann zeta-function's historical significance, from its introduction by Riemann to its enduring legacy in modern mathematics. Learn about the brilliant minds who have dedicated their lives to studying this function, their contributions to the field, and the ongoing pursuit of knowledge that continues to drive research in this captivating area. Join us on this intellectual odyssey as we unravel the enigma of the Riemann zeta-function, embarking on an exploration that promises to expand your horizons, deepen your understanding of mathematics, and ignite your passion for discovery. Prepare to be captivated by the beauty, elegance, and profound implications of this mathematical marvel. If you like this book, write a review!
The Riemann Zeta Function
DOWNLOAD
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.
No detailed description available for "The Riemann Zeta-Function".
An Introduction To The Theory Of The Riemann Zeta Function
DOWNLOAD
Author : S. J. Patterson
language : en
Publisher: Cambridge University Press
Release Date : 1995-02-02
An Introduction To The Theory Of The Riemann Zeta Function written by S. J. Patterson 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 1995-02-02 with Mathematics categories.
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
Spectral Theory Of The Riemann Zeta Function
DOWNLOAD
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 Zeta Function
DOWNLOAD
Author : Aleksandar Ivic
language : en
Publisher: Courier Corporation
Release Date : 2012-07-12
The Riemann Zeta Function written by Aleksandar Ivic and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-12 with Mathematics categories.
This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
The Riemann Hypothesis And The Distribution Of Prime Numbers
DOWNLOAD
Author : Naji Arwashan, PhD, PE
language : en
Publisher: Nova Science Publishers
Release Date : 2021-04-15
The Riemann Hypothesis And The Distribution Of Prime Numbers written by Naji Arwashan, PhD, PE and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis.
Zeta Functions Of Graphs
DOWNLOAD
Author : Audrey Terras
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-18
Zeta Functions Of Graphs written by Audrey Terras 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 2010-11-18 with Mathematics categories.
Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.