Lectures On The Riemann Zeta Function
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Lectures on the Riemann Zeta Function
Author | : H. Iwaniec |
Publsiher | : American Mathematical Society |
Total Pages | : 130 |
Release | : 2014-10-07 |
Genre | : Mathematics |
ISBN | : 9781470418519 |
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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 Mean Values of the Riemann Zeta Function
Author | : A. Ivić |
Publsiher | : Springer |
Total Pages | : 388 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : STANFORD:36105008878543 |
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Lectures on the Mean Value and Omega Theorems for the Riemann Zeta Function
Author | : K. Ramachandra |
Publsiher | : Springer |
Total Pages | : 194 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : UCSC:32106014301722 |
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Zeta Functions over Zeros of Zeta Functions
Author | : André Voros |
Publsiher | : Springer Science & Business Media |
Total Pages | : 171 |
Release | : 2009-11-21 |
Genre | : Mathematics |
ISBN | : 9783642052033 |
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In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.
Prime Numbers and the Riemann Hypothesis
Author | : Barry Mazur,William Stein |
Publsiher | : Cambridge University Press |
Total Pages | : 155 |
Release | : 2016-04-11 |
Genre | : Mathematics |
ISBN | : 9781107101920 |
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This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
The Bloch Kato Conjecture for the Riemann Zeta Function
Author | : John Coates,A. Raghuram,Anupam Saikia,R. Sujatha |
Publsiher | : Cambridge University Press |
Total Pages | : 317 |
Release | : 2015-03-13 |
Genre | : Mathematics |
ISBN | : 9781107492967 |
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A graduate-level account of an important recent result concerning the Riemann zeta function.
The Theory of the Riemann Zeta function
Author | : Late Savilian Professor of Geometry E C Titchmarsh,Edward Charles Titchmarsh,Titchmarsh,D. R. Heath-Brown,Titchmarsh, Edward Charles Titchmarsh |
Publsiher | : Oxford University Press |
Total Pages | : 428 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 0198533691 |
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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.
Lectures on the Riemann Zeta function
Author | : Komaravolu Chandrasekharan |
Publsiher | : Unknown |
Total Pages | : 390 |
Release | : 1962 |
Genre | : Functions, Zeta |
ISBN | : STANFORD:36105031170876 |
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