@article{Wang2022, 
author = {Qian Wang and Xue Han},
title = {Comparing the number of ideals in quadratic number fields},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {4},
pages = {268-271},
keywords = {prime, quadratic number fields, Dedekind zeta function},
url = {https://www.sciopen.com/article/10.3934/mmc.2022025},
doi = {10.3934/mmc.2022025},
abstract = {Denote by        a          K        (  n  ) the number of integral ideals in    K with norm    n, where    K is a algebraic number field of degree    m over the rational field        Q  . Let    p be a prime number. In this paper, we prove that, for two distinct quadratic number fields        K    i    =      Q    (            d      i        )  ,    i  =  1  ,  2, the sets both     {  p        |          a                  K        1              (  p  )  <      a                  K        2              (  p  )  }  and  {  p        |          a                  K        1              (      p    2    )  <      a                  K        2              (      p    2    )  }have analytic density    1      /    4, respectively.}
}