• Corpus ID: 122639371

The Theory of the Riemann Zeta-Function

@inproceedings{Titchmarsh1987TheTO,
  title={The Theory of the Riemann Zeta-Function},
  author={Edward Charles Titchmarsh and D. R. Heath-Brown},
  year={1987}
}
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 heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional… 

Lectures on mean values of the Riemann zeta function

This is an advanced text on the Riemann zeta function, a continuation of the author's earlier book. It presents the most recent results on mean values. An especially detailed discussion is given of

Some identities related to Riemann zeta-function

It is well known that the Riemann zeta-function ζ (s) plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to

Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions

The purpose of the present article is to survey some mean value results obtained recently in zeta-function theory. We do not mention other important aspects of the theory of zeta-functions, such as

Differentiating L-functions

The Riemann zeta function is well known due to its link to prime numbers. The Riemann Xi function is related to the zeta function, and is commonly used due to its nicer analytic properties (such as

Aspects of Analytic Number Theory : The Universality of the Riemann Zeta-Function

Abstract. These notes deal with Voronin’s universality theorem which states, roughly speaking, that any non-vanishing analytic function can be uniformly approximated by certain shifts of the Riemann

The Riemann Zeta Function and Its Analytic Continuation

The objective of this dissertation is to study the Riemann zeta function in particular it will examine its analytic continuation, functional equation and applications. We will begin with some

THE RIEMANN ZETA FUNCTION AND ITS APPLICATION TO NUMBER THEORY

This paper is based on lecture notes given by the second author at Temple University in the spring of 1994. It was in these lectures that the first author was introduced to the theory of the Riemann

On the splitting conjecture in the hybrid model for the Riemann zeta function

The moments of the Riemann zeta function have been the subject of several conjectural methods in recent years. Since the second and fourth moments of Hardy– Littlewood [23] and Ingham [33], it is

The eighth moment of the Riemann zeta function

. In this article, we establish an asymptotic formula for the eighth moment of the Riemann zeta function, assuming the Riemann hypothesis and a quaternary additive divisor conjecture. This builds on

Some identities related to Riemann zeta-function

It is well known that the Riemann zeta-function ζ(s)$\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new
...