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.
Mathematics Subject Classification (2010): 60F05, 11K65
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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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Cellarosi, F., Sinai, Y.G. (2013). Non-standard Limit Theorems in Number Theory. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_10
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DOI: https://doi.org/10.1007/978-3-642-33549-5_10
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