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Author : A. Ivić
Publisher :
ISBN 13 : 9788185198620
Total Pages : 363 pages
Book Rating : 4.1/5 (986 download)
Download or read book Lectures on Mean Values of the Riemann Zeta Function written by A. Ivić and published by . This book was released on 1991 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Ivic
Publisher :
ISBN 13 :
Total Pages : 363 pages
Book Rating : 4.:/5 (927 download)
Download or read book Lectures on Mean Values of the Riemann Zeta Function written by A. Ivic and published by . This book was released on 1991 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K. Ramachandra
Publisher : Springer
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.:/5 (321 download)
Download or read book Lectures on the Mean-Value and Omega Theorems for the Riemann Zeta-Function written by K. Ramachandra and published by Springer. This book was released on 1995 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Ivić
Publisher : Springer
ISBN 13 :
Total Pages : 388 pages
Book Rating : 4.F/5 ( download)
Download or read book Lectures on Mean Values of the Riemann Zeta Function written by A. Ivić and published by Springer. This book was released on 1991 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Iwaniec
Publisher : American Mathematical Society
ISBN 13 : 1470418517
Total Pages : 130 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on the Riemann Zeta Function written by H. Iwaniec and published by American Mathematical Society. This book was released on 2014-10-07 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : A. Ivić
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (651 download)
Download or read book Lectures on Mean Values of the Reimann Zeta Function written by A. Ivić and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yoichi Motohashi
Publisher : Cambridge University Press
ISBN 13 : 0521445205
Total Pages : 246 pages
Book Rating : 4.5/5 (214 download)
Download or read book Spectral Theory of the Riemann Zeta-Function written by Yoichi Motohashi and published by Cambridge University Press. This book was released on 1997-09-11 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : K. Ramachandra
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (318 download)
Download or read book Lectures on the Mean-value and Omega-theorems for the Riemann Zeta-function written by K. Ramachandra and published by . This book was released on 1995 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Edward Charles Titchmarsh
Publisher : Oxford University Press
ISBN 13 : 9780198533696
Total Pages : 428 pages
Book Rating : 4.5/5 (336 download)
Download or read book The Theory of the Riemann Zeta-function written by Edward Charles Titchmarsh and published by Oxford University Press. This book was released on 1986 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.
Author : Kanakanahalli Ramachandra
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (42 download)
Download or read book Riemann Zeta-function written by Kanakanahalli Ramachandra and published by . This book was released on 1979 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anatoly A. Karatsuba
Publisher : Walter de Gruyter
ISBN 13 : 3110886146
Total Pages : 409 pages
Book Rating : 4.1/5 (18 download)
Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 303487023X
Total Pages : 525 pages
Book Rating : 4.0/5 (348 download)
Download or read book Number Theory written by R.P. Bambah and published by Birkhäuser. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Edward Charles Titchmarsh
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Zeta-function of Riemann written by Edward Charles Titchmarsh and published by . This book was released on 1972 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jianqiang Zhao
Publisher : World Scientific
ISBN 13 : 9814689416
Total Pages : 618 pages
Book Rating : 4.8/5 (146 download)
Download or read book Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and published by World Scientific. This book was released on 2016-03-07 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter.
Author : Arthur T. Benjamin
Publisher : American Mathematical Soc.
ISBN 13 : 1470458438
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)
Download or read book Biscuits of Number Theory written by Arthur T. Benjamin and published by American Mathematical Soc.. This book was released on 2020-07-29 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Bohr
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (468 download)
Download or read book Mean-value Theorems for the Riemann Zeta-function written by H. Bohr and published by . This book was released on 1934 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antanas Laurincikas
Publisher : Springer Science & Business Media
ISBN 13 : 9401764018
Total Pages : 192 pages
Book Rating : 4.4/5 (17 download)
Download or read book The Lerch zeta-function written by Antanas Laurincikas and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.
