Biblioteca Allievi della Scuola Superiore di Catania

Contents:

Summary: The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.
The function [zeta](s) and the Dirichlet series related to it --
The analytic character of [zeta](s), and the functional equations --
The theorem of Hadamard and De La Vallée Poussin, and its consequences --
Approximate formulae --
The order of [zeta](s) in the critical strip --
Vinogradov's method --
Mean-value theorems --
[Omega]-theorems --
The general distribution of zeros --
The zeros on the critical line --
The general distribution of values of [zeta](s) --
Divisor problems --
The Lindelöf hypothesis --
Consequences of the Riemann hypothesis --
Calculations relating to the zeros.

Location | Call number | Status | Date due |
---|---|---|---|

515.56 T617 (Browse shelf) | Available |

No cover image available | ||||||||

515.45 T824 Integral equations / | 515.5 L4422 Special functions and their applications / | 515.56 E2641 Riemann's zeta function / | 515.56 T617 The theory of the Riemann zeta-function / | 515.625 G6185 Introduction to difference equations : | 515.63 L9112 Tensors, differential forms, and variational principles / | 515.64 K898 Calcolo delle variazioni / |

Bibliography: p. [392]-412.

The function [zeta](s) and the Dirichlet series related to it --

The analytic character of [zeta](s), and the functional equations --

The theorem of Hadamard and De La Vallée Poussin, and its consequences --

Approximate formulae --

The order of [zeta](s) in the critical strip --

Vinogradov's method --

Mean-value theorems --

[Omega]-theorems --

The general distribution of zeros --

The zeros on the critical line --

The general distribution of values of [zeta](s) --

Divisor problems --

The Lindelöf hypothesis --

Consequences of the Riemann hypothesis --

Calculations relating to the zeros.

The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.