Lectures on Mean Values of the Riemann Zeta Function PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on Mean Values of the Riemann Zeta Function PDF full book. Access full book title Lectures on Mean Values of the Riemann Zeta Function by A. Ivić. Download full books in PDF and EPUB format.
Author: A. Ivić
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Get Book Here
Book Description
Author: A. Ivić
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Get Book Here
Book Description
Author: A. Ivić
Publisher:
ISBN: 9788185198620
Category : Functions, Zeta
Languages : en
Pages : 363
Get Book Here
Book Description
Author: H. Iwaniec
Publisher: American Mathematical Society
ISBN: 1470418517
Category : Mathematics
Languages : en
Pages : 130
Get Book Here
Book Description
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: Yoichi Motohashi
Publisher: Cambridge University Press
ISBN: 0521445205
Category : Mathematics
Languages : en
Pages : 246
Get Book Here
Book Description
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: Anatoly A. Karatsuba
Publisher: Walter de Gruyter
ISBN: 3110886146
Category : Mathematics
Languages : en
Pages : 409
Get Book Here
Book Description
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
Author: R.P. Bambah
Publisher: Birkhäuser
ISBN: 303487023X
Category : Mathematics
Languages : en
Pages : 525
Get Book Here
Book Description
The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.
Author: K. Ramachandra
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 194
Get Book Here
Book Description
Author: Arthur T. Benjamin
Publisher: American Mathematical Soc.
ISBN: 1470458438
Category : Mathematics
Languages : en
Pages : 331
Get Book Here
Book Description
An anthology of articles designed to supplement a first course in number theory.
Author: Eric W. Weisstein
Publisher: CRC Press
ISBN: 1420035223
Category : Mathematics
Languages : en
Pages : 3253
Get Book Here
Book Description
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Author: Aleksandar Ivic
Publisher: Courier Corporation
ISBN: 0486140040
Category : Mathematics
Languages : en
Pages : 548
Get Book Here
Book Description
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.
