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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 zetafunction. 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.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Limit Theorems for the Riemann ZetaFunction
 Authors

 Antanas Laurincikas
 Series Title
 Mathematics and Its Applications
 Series Volume
 352
 Copyright
 1996
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media Dordrecht
 eBook ISBN
 9789401720915
 DOI
 10.1007/9789401720915
 Hardcover ISBN
 9780792338246
 Softcover ISBN
 9789048146475
 Edition Number
 1
 Number of Pages
 XIV, 306
 Topics