Hardy-Ramanujan Journal |

- 1 Institute of Mathematical Sciences [Chennai]
- 2 Queen's University [Kingston, Canada]

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.

Source: HAL:hal-03914203v1

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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