Exploring The Riemann Zeta Function PDF Download
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Author | : Hugh Montgomery |
Publisher | : Springer |
Total Pages | : 298 |
Release | : 2017-09-11 |
Genre | : Mathematics |
ISBN | : 3319599690 |
Download Exploring the Riemann Zeta Function Book in PDF, ePub and Kindle
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.
Author | : Harold M. Edwards |
Publisher | : Courier Corporation |
Total Pages | : 338 |
Release | : 2001-01-01 |
Genre | : Mathematics |
ISBN | : 9780486417400 |
Download Riemann's Zeta Function Book in PDF, ePub and Kindle
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.
Author | : Titchmarch E. C. |
Publisher | : |
Total Pages | : |
Release | : 1992 |
Genre | : |
ISBN | : |
Download Theory of Functions Book in PDF, ePub and Kindle
Author | : H. Iwaniec |
Publisher | : American Mathematical Society |
Total Pages | : 130 |
Release | : 2014-10-07 |
Genre | : Mathematics |
ISBN | : 1470418517 |
Download Lectures on the Riemann Zeta Function Book in PDF, ePub and Kindle
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.
Author | : Aleksandar Ivic |
Publisher | : Courier Corporation |
Total Pages | : 548 |
Release | : 2012-07-12 |
Genre | : Mathematics |
ISBN | : 0486140040 |
Download The Riemann Zeta-Function Book in PDF, ePub and Kindle
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.
Author | : Michel Laurent Lapidus |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821842225 |
Download In Search of the Riemann Zeros Book in PDF, ePub and Kindle
Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.
Author | : Peter B. Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 543 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0387721258 |
Download The Riemann Hypothesis Book in PDF, ePub and Kindle
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.
Author | : Naji Arwashan, PhD, PE |
Publisher | : Nova Science Publishers |
Total Pages | : 232 |
Release | : 2021-04-15 |
Genre | : Mathematics |
ISBN | : 1536194220 |
Download The Riemann Hypothesis and the Distribution of Prime Numbers Book in PDF, ePub and Kindle
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.
Author | : Barry Mazur |
Publisher | : Cambridge University Press |
Total Pages | : 155 |
Release | : 2016-04-11 |
Genre | : Mathematics |
ISBN | : 1107101921 |
Download Prime Numbers and the Riemann Hypothesis Book in PDF, ePub and Kindle
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Author | : Dan Rockmore |
Publisher | : Vintage |
Total Pages | : 306 |
Release | : 2006-05-09 |
Genre | : Mathematics |
ISBN | : 0375727728 |
Download Stalking the Riemann Hypothesis Book in PDF, ePub and Kindle
For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.