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A localized Erdős-Kac theorem

Abstract : Let ω_y (n) be the number of distinct prime divisors of n not exceeding y. If y_n is an increasing function of n such that log y_n = o(log n), we study the distribution of ω_{y_n} (n) and establish an analog of the Erdős-Kac theorem for this function. En route, we also prove a variant central limit theorem for random variables, which are not necessarily independent, but are well approximated by independent random variables.
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https://hal.archives-ouvertes.fr/hal-03208199
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Submitted on : Monday, April 26, 2021 - 1:17:25 PM
Last modification on : Tuesday, May 11, 2021 - 10:47:59 AM
Long-term archiving on: : Tuesday, July 27, 2021 - 6:59:28 PM

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Anup B Dixit, M Ram Murty. A localized Erdős-Kac theorem. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan, pp.17 - 23. ⟨hal-03208199⟩

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