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Author :
Publisher :
ISBN 13 : 9780387584379
Total Pages : 169 pages
Book Rating : 4.5/5 (843 download)
Download or read book Lectures on On the Mean-value and Omega-theorems for the Riemann Zeta-function written by and published by . This book was released on 1995 with total page 169 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 : 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 : 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. 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 : 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 : Komaravolu Chandrasekharan
Publisher :
ISBN 13 :
Total Pages : 390 pages
Book Rating : 4.F/5 ( download)
Download or read book Lectures on the Riemann Zeta-function written by Komaravolu Chandrasekharan and published by . This book was released on 1962 with total page 390 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.
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 : Komaravolu Chandrasekharan (mathematician)
Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (117 download)
Download or read book Lectures on the Riemann Zeta-function written by Komaravolu Chandrasekharan (mathematician) and published by . This book was released on 1953 with total page 304 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 : Komaravolu Chandrasekharan (Mathematician, India, Switzerland)
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (637 download)
Download or read book Lectures on the Riemann Zeta-Function written by Komaravolu Chandrasekharan (Mathematician, India, Switzerland) and published by . This book was released on 1953 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Coates
Publisher : Cambridge University Press
ISBN 13 : 1107492963
Total Pages : 317 pages
Book Rating : 4.1/5 (74 download)
Download or read book The Bloch-Kato Conjecture for the Riemann Zeta Function written by John Coates and published by Cambridge University Press. This book was released on 2015-03-13 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level account of an important recent result concerning the Riemann zeta function.
Author : International Business Machines Corporation. Research Division
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (123 download)
Download or read book On Some Mean Value Results for the Riemann Zeta-function written by International Business Machines Corporation. Research Division and published by . This book was released on 1987 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter B. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387721258
Total Pages : 543 pages
Book Rating : 4.3/5 (877 download)
Download or read book The Riemann Hypothesis written by Peter B. Borwein and published by Springer Science & Business Media. This book was released on 2008 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
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 : Aleksandar Ivic
Publisher : Dover Publications
ISBN 13 : 9780486789019
Total Pages : 562 pages
Book Rating : 4.7/5 (89 download)
Download or read book The Riemann Zeta-Function written by Aleksandar Ivic and published by Dover Publications. This book was released on 2013-12-23 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A thorough and easily accessible account." -- MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.
