JIPAM logo: Home Link
Home Editors Submissions Reviews Volumes RGMIA About Us

  Volume 9, Issue 1, Article 12
Properties of Some Functions Connected to Prime Numbers

    Authors: Gabriel Mincu, Laurentiu Panaitopol,  
    Keywords: Arithmetic functions, Inequalities, Landau's inequality, Additivity, Multiplicativity.  
    Date Received: 08/09/2007  
    Date Accepted: 16/11/2007  
    Subject Codes:

11N64, 11Y70, 11N05.

    Editors: László Tóth,  

Let $ theta$ and $ psi$ be the Chebyshev functions. We denote $ psi_2(x)=psi(x)-theta(x)$ and $ rho(x)=psi(x)/theta(x)$. We study subadditive and Landau-type properties for $ theta, psi,$ and $ psi_2$. We show that $ rho$ is subadditive and submultiplicative. Finally, we consider the prime counting function $ pi(x)$ and show that

  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page

      search [advanced search] copyright 2003 terms and conditions login