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Riemann's Zeta Function

2001-01-01 Mathematics
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Release : 2001-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 400/5 ( reviews)

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Book Synopsis Riemann's Zeta Function by : Harold M. Edwards

Download or read book Riemann's Zeta Function written by Harold M. Edwards. This book was released on 2001-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

2014-10-07 Mathematics
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Release : 2014-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 517/5 ( reviews)

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Book Synopsis Lectures on the Riemann Zeta Function by : H. Iwaniec

Download or read book Lectures on the Riemann Zeta Function written by H. Iwaniec. This book was released on 2014-10-07. Available in PDF, EPUB and Kindle. Book excerpt: 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

2011-05-03 Mathematics
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Release : 2011-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 146/5 ( reviews)

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Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba

Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba. This book was released on 2011-05-03. 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

The Riemann Hypothesis and the Roots of the Riemann Zeta Function

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 385/5 ( reviews)

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Book Synopsis The Riemann Hypothesis and the Roots of the Riemann Zeta Function by : Samuel W. Gilbert

Download or read book The Riemann Hypothesis and the Roots of the Riemann Zeta Function written by Samuel W. Gilbert. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exploring the Riemann Zeta Function

2017-09-11 Mathematics
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Release : 2017-09-11
Genre : Mathematics
Kind : eBook
Book Rating : 690/5 ( reviews)

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Book Synopsis Exploring the Riemann Zeta Function by : Hugh Montgomery

Download or read book Exploring the Riemann Zeta Function written by Hugh Montgomery. This book was released on 2017-09-11. 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.

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