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 ;

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