Non-standard Limit Theorems in Number Theory

  • Francesco Cellarosi
  • Yakov G. Sinai
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 33)


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.


Möbius function Limit theorems Infinite divisibility Dickman-De Bruijn distribution 



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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