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Mathematics and Its Applications

Limit Theorems for the Riemann Zeta-Function

Authors: Laurincikas, Antanas

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eBook 91,62 €
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  • ISBN 978-94-017-2091-5
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Hardcover 114,39 €
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  • ISBN 978-0-7923-3824-6
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Softcover 163,28 €
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  • ISBN 978-90-481-4647-5
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About this book

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.

Table of contents (9 chapters)

  • Elements of the Probability Theory

    Laurinčikas, Antanas

    Pages 1-25

    Preview Buy Chapter 30,19 €
  • Dirichlet Series and Dirichlet Polynomials

    Laurinčikas, Antanas

    Pages 26-86

    Preview Buy Chapter 30,19 €
  • Limit Theorems for the Modulus of the Riemann Zeta-Function

    Laurinčikas, Antanas

    Pages 87-148

    Preview Buy Chapter 30,19 €
  • Limit Theorems for the Riemann Zeta-Function on the Complex Plane

    Laurinčikas, Antanas

    Pages 149-178

    Preview Buy Chapter 30,19 €
  • Limit Theorems for the Riemann Zeta-Function in the Space of Analytic Functions

    Laurinčikas, Antanas

    Pages 179-202

    Preview Buy Chapter 30,19 €

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-94-017-2091-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-7923-3824-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 163,28 €
price for Spain (gross)
  • ISBN 978-90-481-4647-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Limit Theorems for the Riemann Zeta-Function
Authors
Series Title
Mathematics and Its Applications
Series Volume
352
Copyright
1996
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-2091-5
DOI
10.1007/978-94-017-2091-5
Hardcover ISBN
978-0-7923-3824-6
Softcover ISBN
978-90-481-4647-5
Edition Number
1
Number of Pages
XIV, 306
Topics