Anup Dixit ; M Murty - A localized Erdős-Kac theorem for ωy(p+a)

hrj:10907 - Hardy-Ramanujan Journal, February 6, 2023, Volume 45 - 2022 - https://doi.org/10.46298/hrj.2023.10907
A localized Erdős-Kac theorem for ωy(p+a)Article

Authors: Anup Dixit 1; M Murty 2

Let ωy(n) denote the number of distinct prime divisors of n less than y. Suppose yn is an increasing sequence of positive real numbers satisfying logyn=o(loglogn). In this paper, we prove an Erdös-Kac theorem for the distribution of ωyn(p+a), where p runs over all prime numbers and a is a fixed integer. We also highlight the connection between the distribution of ωy(p1) and Ihara's conjectures on Euler-Kronecker constants.


Volume: Volume 45 - 2022
Published on: February 6, 2023
Imported on: February 6, 2023
Keywords: Erdős-Kac Theorem,Euler-Kronecker constant,[MATH]Mathematics [math]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada

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