Non-standard Limit Theorems in Number Theory

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 33)

Abstract

We prove a non-standard limit theorem for a sequence of random variables connected with the classical Möbius function. The so-called Dickman-De Bruijn distribution appears in the limit. We discuss some of its properties, and we provide a number of estimates for the error term in the limit theorem.

Keywords

Möbius function Limit theorems Infinite divisibility Dickman-De Bruijn distribution 

Notes

Acknowledgements

We would like to thank Alex Kontorovich and Andrew Granville for useful discussions and comments. The second author acknowledges the financial support from the NSF Grant 0600996.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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