Lectures On The Riemann Zeta Functions PDF Download
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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 | : Komaravolu Chandrasekharan |
Publisher | : |
Total Pages | : 304 |
Release | : 1953 |
Genre | : Functions, Zeta |
ISBN | : |
Download Lectures on the Riemann Zeta-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 | : Komaravolu Chandrasekharan |
Publisher | : |
Total Pages | : 390 |
Release | : 1962 |
Genre | : Functions, Zeta |
ISBN | : |
Download Lectures on the Riemann Zeta-function Book in PDF, ePub and Kindle
Author | : Komaravolu Chandrasekharan (mathematician) |
Publisher | : |
Total Pages | : 304 |
Release | : 1953 |
Genre | : Functions, Zeta |
ISBN | : |
Download Lectures on the Riemann Zeta-function Book in PDF, ePub and Kindle
Author | : K. Ramachandra |
Publisher | : |
Total Pages | : 200 |
Release | : 1995 |
Genre | : Functions, Zeta |
ISBN | : |
Download Lectures on the Mean-value and Omega-theorems for the Riemann Zeta-function Book in PDF, ePub and Kindle
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 | : A. Ivić |
Publisher | : Springer |
Total Pages | : 388 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
Download Lectures on Mean Values of the Riemann Zeta Function Book in PDF, ePub and Kindle
Author | : André Voros |
Publisher | : Springer Science & Business Media |
Total Pages | : 171 |
Release | : 2009-11-21 |
Genre | : Mathematics |
ISBN | : 3642052037 |
Download Zeta Functions over Zeros of Zeta Functions Book in PDF, ePub and Kindle
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.
Author | : Marcus du Sautoy |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 354074701X |
Download Zeta Functions of Groups and Rings Book in PDF, ePub and Kindle
Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.