Limit Theorems for the Riemann Zeta-Function

Laurincikas, Antanas

ISBN 10: 0792338243 / ISBN 13: 9780792338246

Published by Springer, 1995

Unread book in perfect condition. Seller Inventory # 4356966

Synopsis:

The subject of this book is probabilistic number theory. In a wide sense probabilistic number theory is part of the analytic number theory, where the methods and ideas of probability theory are used to study the distribution of values of arithmetic objects. This is usually complicated, as it is difficult to say anything about their concrete values. This is why the following problem is usually investigated: given some set, how often do values of an arithmetic object get into this set? It turns out that this frequency follows strict mathematical laws. Here we discover an analogy with quantum mechanics where it is impossible to describe the chaotic behaviour of one particle, but that large numbers of particles obey statistical laws. The objects of investigation of this book are Dirichlet series, and, as the title shows, the main attention is devoted to the Riemann zeta-function. In studying the distribution of values of Dirichlet series the weak convergence of probability measures on different spaces (one of the principle asymptotic probability theory methods) is used. The application of this method was launched by H. Bohr in the third decade of this century and it was implemented in his works together with B. Jessen. Further development of this idea was made in the papers of B. Jessen and A. Wintner, V. Borchsenius and B.

Synopsis: This volume presents a range of results in analytic and probabilistic number theory. The full spectrum of limit theorems in the sense of weak convergence of probability measures for the modules of the Riemann zeta-function and other functions is given by Dirichlet series. Applications to the universality and functional independence of such functions are also given. Furthermore, similar results are presented for Dirichlet L-functions and Dirichlet series with multiplicative coefficients. This is a self-contained book, which should be useful for researchers and graduate students working in analytic and probabilistic number theory and can also be used as a textbook for postgraduate courses.

Bibliographic Details

Title: Limit Theorems for the Riemann Zeta-Function
Publisher: Springer
Publication Date: 1995
Binding: Hardcover
Condition: As New