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

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 $\omega_y(p+a)$Article

Authors: Anup Dixit 1; M Murty 2

Let $\omega_y(n)$ denote the number of distinct prime divisors of $n$ less than $y$. Suppose $y_n$ is an increasing sequence of positive real numbers satisfying $\log y_n = o(\log\log n)$. In this paper, we prove an Erdös-Kac theorem for the distribution of $\omega_{y_n}(p+a)$, where $p$ runs over all prime numbers and $a$ is a fixed integer. We also highlight the connection between the distribution of $\omega_y(p-1)$ 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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