Limit Theorems for the Riemann Zeta-Function:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
352 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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. |
| Beschreibung: | 1 Online-Ressource (XIV, 306 p) |
| ISBN: | 9789401720915 9789048146475 |
| DOI: | 10.1007/978-94-017-2091-5 |
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| institution | BVB |
| isbn | 9789401720915 9789048146475 |
| language | English |
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| spelling | Laurinčikas, Antanas Verfasser aut Limit Theorems for the Riemann Zeta-Function by Antanas Laurinčikas Dordrecht Springer Netherlands 1996 1 Online-Ressource (XIV, 306 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 352 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. Mathematics Functional analysis Functions of complex variables Number theory Distribution (Probability theory) Number Theory Probability Theory and Stochastic Processes Functions of a Complex Variable Functional Analysis Measure and Integration Mathematik Riemannsche Zetafunktion (DE-588)4308419-9 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Riemannsche Zetafunktion (DE-588)4308419-9 s Grenzwertsatz (DE-588)4158163-5 s 1\p DE-604 https://doi.org/10.1007/978-94-017-2091-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Laurinčikas, Antanas Limit Theorems for the Riemann Zeta-Function Mathematics Functional analysis Functions of complex variables Number theory Distribution (Probability theory) Number Theory Probability Theory and Stochastic Processes Functions of a Complex Variable Functional Analysis Measure and Integration Mathematik Riemannsche Zetafunktion (DE-588)4308419-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4308419-9 (DE-588)4158163-5 |
| title | Limit Theorems for the Riemann Zeta-Function |
| title_auth | Limit Theorems for the Riemann Zeta-Function |
| title_exact_search | Limit Theorems for the Riemann Zeta-Function |
| title_full | Limit Theorems for the Riemann Zeta-Function by Antanas Laurinčikas |
| title_fullStr | Limit Theorems for the Riemann Zeta-Function by Antanas Laurinčikas |
| title_full_unstemmed | Limit Theorems for the Riemann Zeta-Function by Antanas Laurinčikas |
| title_short | Limit Theorems for the Riemann Zeta-Function |
| title_sort | limit theorems for the riemann zeta function |
| topic | Mathematics Functional analysis Functions of complex variables Number theory Distribution (Probability theory) Number Theory Probability Theory and Stochastic Processes Functions of a Complex Variable Functional Analysis Measure and Integration Mathematik Riemannsche Zetafunktion (DE-588)4308419-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Mathematics Functional analysis Functions of complex variables Number theory Distribution (Probability theory) Number Theory Probability Theory and Stochastic Processes Functions of a Complex Variable Functional Analysis Measure and Integration Mathematik Riemannsche Zetafunktion Grenzwertsatz |
| url | https://doi.org/10.1007/978-94-017-2091-5 |
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