@article{Wei2024, 
author = {Tong Wei},
title = {The distribution of ideals whose norm divides    n in the Gaussian ring},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {5863-5876},
keywords = {Selberg-Delange method, the distribution, Gaussian ring, beta distribution},
url = {https://www.sciopen.com/article/10.3934/math.2024285},
doi = {10.3934/math.2024285},
abstract = {Let        O          K        =      Z    [  i  ]. For each positive integer    n, denote        ξ          K        (  n  ) as the number of integral ideals whose norm divides    n in        O          K      . In this paper, we studied the distribution of ideals whose norm divides    n in        O          K       by using the Selberg-Delange method. This is a natural variant of a result studied by Deshouillers, Dress, and Tenenbaum (often called the DDT Theorem), and we found that the distribution function was subject to beta distribution with density        3        /    (  2  π                    u                  2                    (      1      −      u      )        3    ).}
}