Lectures On The Riemann Zeta Function
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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.
Lectures On The Riemann Zeta Function
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Author : Komaravolu Chandrasekharan (mathematician)
language : en
Publisher:
Release Date : 1953
Lectures On The Riemann Zeta Function written by Komaravolu Chandrasekharan (mathematician) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Functions, Zeta categories.
Lectures On The Riemann Zeta Function
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Author : Komaravolu Chandrasekharan
language : en
Publisher:
Release Date : 1953
Lectures On The Riemann Zeta Function written by Komaravolu Chandrasekharan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Functions categories.
Lectures On The Riemann Zeta Function
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Author : Komaravolu Chandrasekharan (Mathematician, India, Switzerland)
language : en
Publisher:
Release Date : 1953
Lectures On The Riemann Zeta Function written by Komaravolu Chandrasekharan (Mathematician, India, Switzerland) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with categories.
Lectures On Mean Values Of The Riemann Zeta Function
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Author : A. Ivić
language : en
Publisher: Springer Verlag
Release Date : 1991
Lectures On Mean Values Of The Riemann Zeta Function written by A. Ivić and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This is an advanced text on the Riemann zeta-function, a continuation of theauthor's earlier book. It presents the most recent results on mean values, many of which had not yet appeared in print at the time of the writing of the text. An especially detailed discussion is given of the second and the fourth moment, and the latter is studied by the use of spectral theory, one of the most powerful methods used lately in analytic number theory. The book presupposes a reasonable knowledge of zeta-function theory and complex analysis. It will be of great use to the researchers in the field, an to all those who wish to get well acquainted with the subject or who have the need for application of zeta-function theory.
The Riemann Zeta Function
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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.
Lectures On The Mean Value And Omega Theorems For The Riemann Zeta Function
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Author : K. Ramachandra
language : en
Publisher: Springer
Release Date : 1995
Lectures On The Mean Value And Omega Theorems For The Riemann Zeta Function written by K. Ramachandra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Lectures On The Riemann Zeta Functions
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Author : Komaravolu Chandrasekharan
language : en
Publisher:
Release Date : 1953
Lectures On The Riemann Zeta Functions written by Komaravolu Chandrasekharan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Functions, Zeta categories.
Prime Numbers And The Riemann Hypothesis
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Author : Barry Mazur
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-11
Prime Numbers And The Riemann Hypothesis written by Barry Mazur 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 2016-04-11 with Mathematics categories.
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
The Riemann Hypothesis
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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
The Riemann Hypothesis written by Peter B. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.