Zeta Functions

Author : Harold M. Edwards
Publisher : Courier Corporation
ISBN 13 : 9780486417400
Total Pages : 338 pages
Book Rating : 4.09/5 ( download)

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Download or read book Riemann's Zeta Function written by Harold M. Edwards and published by Courier Corporation. This book was released on 2001-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.

Author : Aleksandar Ivic
Publisher : Courier Corporation
ISBN 13 : 0486140040
Total Pages : 548 pages
Book Rating : 4.49/5 ( download)

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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 : Roger Godement
Publisher : Springer
ISBN 13 : 3540374361
Total Pages : 200 pages
Book Rating : 4.67/5 ( download)

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Download or read book Zeta Functions of Simple Algebras written by Roger Godement and published by Springer. This book was released on 2006-11-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Audrey Terras
Publisher : Cambridge University Press
ISBN 13 : 1139491784
Total Pages : 253 pages
Book Rating : 4.85/5 ( download)

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Download or read book Zeta Functions of Graphs written by Audrey Terras and published by Cambridge University Press. This book was released on 2010-11-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.

Author : Antanas Laurincikas
Publisher : Springer Science & Business Media
ISBN 13 : 9401764018
Total Pages : 192 pages
Book Rating : 4.18/5 ( download)

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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 : Titchmarch E. C.
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.46/5 ( download)

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Download or read book Theory of Functions written by Titchmarch E. C. and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Hari M. Srivastava
Publisher : Springer Science & Business Media
ISBN 13 : 9780792370543
Total Pages : 408 pages
Book Rating : 4.46/5 ( download)

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Download or read book Series Associated With the Zeta and Related Functions written by Hari M. Srivastava and published by Springer Science & Business Media. This book was released on 2001 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.

Author : Bruno Kahn
Publisher : Cambridge University Press
ISBN 13 : 1108574912
Total Pages : 217 pages
Book Rating : 4.14/5 ( download)

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Download or read book Zeta and L-Functions of Varieties and Motives written by Bruno Kahn and published by Cambridge University Press. This book was released on 2020-05-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.

Author : Tsuneo Arakawa
Publisher : Springer
ISBN 13 : 4431549196
Total Pages : 278 pages
Book Rating : 4.92/5 ( download)

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Download or read book Bernoulli Numbers and Zeta Functions written by Tsuneo Arakawa and published by Springer. This book was released on 2014-07-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.

Author : H. M. Srivastava
Publisher : Elsevier
ISBN 13 : 0123852188
Total Pages : 675 pages
Book Rating : 4.82/5 ( download)

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Download or read book Zeta and Q-Zeta Functions and Associated Series and Integrals written by H. M. Srivastava and published by Elsevier. This book was released on 2011-10-25 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions