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Author | : Late Savilian Professor of Geometry E C Titchmarsh |
Publisher | : Oxford University Press |
Total Pages | : 428 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 9780198533696 |
Download The Theory of the Riemann Zeta-function Book in PDF, ePub and Kindle
The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.
Author | : Titchmarch E. C. |
Publisher | : |
Total Pages | : |
Release | : 1992 |
Genre | : |
ISBN | : |
Download Theory of Functions Book in PDF, ePub and Kindle
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 | : S. J. Patterson |
Publisher | : Cambridge University Press |
Total Pages | : 176 |
Release | : 1995-02-02 |
Genre | : Mathematics |
ISBN | : 9780521499057 |
Download An Introduction to the Theory of the Riemann Zeta-Function Book in PDF, ePub and Kindle
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
Author | : Yoichi Motohashi |
Publisher | : Cambridge University Press |
Total Pages | : 246 |
Release | : 1997-09-11 |
Genre | : Mathematics |
ISBN | : 0521445205 |
Download Spectral Theory of the Riemann Zeta-Function Book in PDF, ePub and Kindle
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.
Author | : Aleksandar Ivic |
Publisher | : Courier Corporation |
Total Pages | : 548 |
Release | : 2012-07-12 |
Genre | : Mathematics |
ISBN | : 0486140040 |
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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 | : 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 | : |
Publisher | : |
Total Pages | : 346 |
Release | : 1951 |
Genre | : |
ISBN | : |
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Author | : Antanas Laurincikas |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401720916 |
Download Limit Theorems for the Riemann Zeta-Function Book in PDF, ePub and Kindle
The subject of this book is probabilistic number theory. In a wide sense probabilistic number theory is part of the analytic number theory, where the methods and ideas of probability theory are used to study the distribution of values of arithmetic objects. This is usually complicated, as it is difficult to say anything about their concrete values. This is why the following problem is usually investigated: given some set, how often do values of an arithmetic object get into this set? It turns out that this frequency follows strict mathematical laws. Here we discover an analogy with quantum mechanics where it is impossible to describe the chaotic behaviour of one particle, but that large numbers of particles obey statistical laws. The objects of investigation of this book are Dirichlet series, and, as the title shows, the main attention is devoted to the Riemann zeta-function. In studying the distribution of values of Dirichlet series the weak convergence of probability measures on different spaces (one of the principle asymptotic probability theory methods) is used. The application of this method was launched by H. Bohr in the third decade of this century and it was implemented in his works together with B. Jessen. Further development of this idea was made in the papers of B. Jessen and A. Wintner, V. Borchsenius and B.
Author | : Edward Charles Titchmarsh |
Publisher | : |
Total Pages | : 454 |
Release | : 1960 |
Genre | : Functions, Zeta |
ISBN | : |
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