Non-standard limit theorems in number theory

Francesco Cellarosi, Yakov G. Sinai

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProkhorov and Contemporary Probability Theory
Subtitle of host publicationIn Honor of Yuri V. Prokhorov
Pages197-213
Number of pages17
DOIs
StatePublished - Sep 3 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume33
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Dickman-De Bruijn distribution
  • Infinite divisibility
  • Limit theorems
  • Möbius function

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