Lectures 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.

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.

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.

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.

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.

Hardy Ramanujan Journal

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Author :
language : en
Publisher:
Release Date : 1988

Hardy Ramanujan Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Number theory categories.

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.

Introduction To Finite And Infinite Dimensional Lie Super Algebras

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Author : Neelacanta Sthanumoorthy
language : en
Publisher: Academic Press
Release Date : 2016-04-26

Introduction To Finite And Infinite Dimensional Lie Super Algebras written by Neelacanta Sthanumoorthy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Mathematics categories.

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