Lectures On On The Mean Value And Omega Theorems For The Riemann Zeta Function
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Lectures On On The Mean Value And Omega Theorems For The Riemann Zeta Function
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Author :
language : en
Publisher:
Release Date : 1995
Lectures On On The Mean Value And Omega Theorems For The Riemann Zeta Function written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Functions, Zeta categories.
Lectures On The Mean Value And Omega Theorems For The Riemann Zeta Function
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Author : K. Ramachandra
language : en
Publisher:
Release Date : 1995
Lectures On The Mean Value And Omega Theorems For The Riemann Zeta Function written by K. Ramachandra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Functions, Zeta categories.
The Lerch Zeta Function
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Author : Antanas Laurincikas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
The Lerch Zeta Function written by Antanas Laurincikas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
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.
The Riemann Hypothesis
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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
The Riemann Hypothesis written by Peter B. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Selected Of Norman Levinson
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Author : Norman Levinson
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Selected Of Norman Levinson written by Norman Levinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology.
Lectures On Mean Values Of The Riemann Zeta Function
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Author : A. Ivić
language : en
Publisher: Springer Verlag
Release Date : 1991
Lectures On Mean Values Of The Riemann Zeta Function written by A. Ivić and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This is an advanced text on the Riemann zeta-function, a continuation of theauthor's earlier book. It presents the most recent results on mean values, many of which had not yet appeared in print at the time of the writing of the text. An especially detailed discussion is given of the second and the fourth moment, and the latter is studied by the use of spectral theory, one of the most powerful methods used lately in analytic number theory. The book presupposes a reasonable knowledge of zeta-function theory and complex analysis. It will be of great use to the researchers in the field, an to all those who wish to get well acquainted with the subject or who have the need for application of zeta-function theory.
Number Theory
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Author : R.P. Bambah
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Number Theory written by R.P. Bambah and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Acta Arithmetica
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Author :
language : en
Publisher:
Release Date : 2014
Acta Arithmetica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
Lectures On Quantum Computation Quantum Error Correcting Codes And Information Theory
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Author : K. R. Parthasarathy
language : en
Publisher:
Release Date : 2006
Lectures On Quantum Computation Quantum Error Correcting Codes And Information Theory written by K. R. Parthasarathy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
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.
Research Schools On Number Theory In India
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Author : Purabi Mukherji
language : en
Publisher: Springer Nature
Release Date : 2021-01-05
Research Schools On Number Theory In India written by Purabi Mukherji and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-05 with Mathematics categories.
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.