Last edited by Shakticage

Monday, August 10, 2020 | History

2 edition of **Zeta function theory** found in the catalog.

Zeta function theory

Cem Yalcin Yildirim

- 302 Want to read
- 38 Currently reading

Published
**1990**
by [s.n.] in Toronto
.

Written in English

**Edition Notes**

Statement | Cem Yalcin Yildirim. |

ID Numbers | |
---|---|

Open Library | OL17066949M |

The standard works in this field are Titchmarsh’s The Theory of the Riemann Zeta Function and Ivić’s The Riemann Zeta Function: Advances continue to be made in our knowledge of the zeta function, and none of these books (all 20 to 30 years old) is very up-to-date today, but the present book is still very valuable as an introduction. The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann /5(7).

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. The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, Brand: Oxford University Press.

The principal problem in the theory of the zeta-function is the problem of the location of its non-trivial zeros and, in general, of its values within the range $1/2\leq \sigma\leq 1$. The main directions of research conducted on the zeta-function include: the determination of the widest possible domain to the left of the straight line $\sigma. 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.

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Zeta function. This book contains a lot of application, theory, and, to my surprise, several practice problems at the end of each section to maximize the learning experience. The chapters are concise and the mathematics is relatively easy follow for those with some experience in special by: Reviewed in the United States on J this is book is an udpate of the book of titchmarsh (the theory of the riemann zeta Zeta function theory book.

it covers all the results from to (up to atkinson's formula). if you are looking for stuff about prime numbers, or the prime number distribution, this book will only cover a tiny bit/5(7). The Riemann Zeta-Function book. Read reviews from world’s largest community for readers. Comprehensive and coherent, this text covers exponential integra The Riemann Zeta-Function book/5(7).

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 Zeta function theory book estimates over short intervals, higher power moments, and omega results.

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory.4/5(6).

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 Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers.

This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its s: 2. - Buy The Theory of the Riemann Zeta-Function (Oxford Science Publications) book online at best prices in India on Read The Theory of the Riemann Zeta-Function (Oxford Science Publications) book reviews & author details Reviews: Titchmarsh assumes the reader is skilled in complex variable theory at the level of his text "The Theory of Functions" and also assumes you know the product expansion of the Zeta-Function in terms of the primes (1st page!-can be found in Hardy-Wright or online, involves geometric series') Hardy's Theorem on the zeroes of Zeta on the critical line is proven in this text and this is referenced Reviews: "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 4/5(2).

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and. This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function.

Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number by: About this book. This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July in Hildesheim, Germany.

Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number.

The Theory of the Riemann Zeta-function (2nd ed.). Oxford: Oxford Science Publications. 21– ISBN Attributed to Bernhard zero: −, 1, 2, {\displaystyle -{\frac {1}{2}}}. Contributors; The Riemann zeta function \(\zeta(z)\) is an analytic function that is a very important function in analytic number theory.

It is (initially) defined in some domain in the complex plane by the special type of Dirichlet series given by \[\zeta(z)=\sum_{n=1}^{\infty}\frac{1}{n^z},\] where \(Re(z)>1\). It can be readily verified that the given series converges locally uniformly, and.

It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension.

Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The Riemann zeta function at 0 and 1. At zero, one has = − = − + = −At 1 there is a pole, so ζ(1) is not finite but the left and right limits are: → ± (+) = ± ∞ Since it is a pole of first order, its principal value exists and is equal to the Euler–Mascheroni constant γ = +.

Positive integers Even positive integers. For the even positive integers, one has the. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory.

Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number : $ 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 Brand: Dover Publications.

Superb study of one of the most influential classics in mathematics examines the landmark 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.

"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 Author: Aleksandar Ivic.Riemann zeta-function and the theory of the distribution of primes. Acta. Mathematica, 41(1), – The book is, without any doubt, the most up-to-date, systematic, and theoretically.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.