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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 : 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 : 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 : 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 : Purabi Mukherji
Publisher : Springer Nature
ISBN 13 : 9811596204
Total Pages : 187 pages
Book Rating : 4.8/5 (115 download)
Download or read book Research Schools on Number Theory in India written by Purabi Mukherji and published by Springer Nature. This book was released on 2021-01-05 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar—including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.
Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
ISBN 13 : 012804683X
Total Pages : 512 pages
Book Rating : 4.1/5 (28 download)
Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras
Author : Aleksandar Ivic
Publisher : Courier Corporation
ISBN 13 : 0486140040
Total Pages : 548 pages
Book Rating : 4.4/5 (861 download)
Download or read book The Riemann Zeta-Function written by Aleksandar Ivic and published by Courier Corporation. This book was released on 2012-07-12 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :
Publisher :
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.3/5 (91 download)
Download or read book Journal de théorie des nombres de Bordeaux written by and published by . This book was released on 1996 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 788 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 1997 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ram Prakash Bambah
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)
Download or read book Number Theory written by Ram Prakash Bambah and published by . This book was released on 2000 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Bahuguna
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842650943
Total Pages : 204 pages
Book Rating : 4.6/5 (59 download)
Download or read book Topics in Sobolev Spaces and Applications written by D. Bahuguna and published by Alpha Science Int'l Ltd.. This book was released on 2002 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers the Sobolev spaces and their applications to many areas of differential equations. It deals with some basic results on Sobolev spaces, density theorems, and approximation theorems and embedding theorems.
Author : K. R. Parthasarathy
Publisher : Narosa Publishing House
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (321 download)
Download or read book Lectures on Quantum Computation, Quantum Error Correcting Codes and Information Theory written by K. R. Parthasarathy and published by Narosa Publishing House. This book was released on 2006 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. The topics include a comparative description of the basic features of classical probability theory on finite sample spaces and quantum probability theory on finite dimensional complex Hilbert spaces, quantum gates and cicuits, simple examples of circuits arising from quantum teleportation, communication through EPR pairs and arithmetical computations on a quantum computer, more sophisticated examples of such circuits in the context of Fourier transform and phase estimation, a detailed account of the order finding algorithm as well as the celebrated Shor's algorithm for factorising a positive integer into its prime factors. There is a leisurely discussion of quantum error correcting codes with the Knill-Laflamme criterion for error correction and a number of examples of such codes whose construction is based on the Weyl commutation relations for finite abelian groups. The reader may find here a brief introduction to the basic ideas of classical information theory as developed by Shannon,properties of von Neumann's quantum entropy and relative entropy as well as a proof of Schumacher's noiseless quantum coding theorem. The Holevo bound for transmission of classical information through encoding by quantum states followed by measurements is derived. The only background assumed of the reader is linear algebra on finite dimensional complex vector spaces and elementary classical probability theory on finite sample spaces.These notes are aimed at mathematicians and computer scientists who are curious to know the mystery behind a quantum computer and the possibility of communicating information using the principles of elementary quantum theory.
Author : F. Thomas Farrell
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (321 download)
Download or read book Lectures on Surgical Methods in Rigidity written by F. Thomas Farrell and published by . This book was released on 1996 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.:/5 (318 download)
Download or read book Acta arithmetica written by and published by . This book was released on 2014 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henryk Iwaniec
Publisher :
ISBN 13 : 9781470418915
Total Pages : 119 pages
Book Rating : 4.4/5 (189 download)
Download or read book Lectures on the Riemann Zeta Function written by Henryk Iwaniec and published by . This book was released on 2014 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
