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  Volume 3, Issue 3, Article 37
 
On an Inequality Related to the Legendre Totient Function

    Authors: Pentti Haukkanen,  
    Keywords: Legendre totient function, Inequality, Regular convolution, Unitary convolution.  
    Date Received: 06/02/02  
    Date Accepted: 27/02/02  
    Subject Codes:

11A25

 
    Editors: Jozsef Sandor,  
 
    Abstract:

Let $Delta(x, n)=varphi(x, n)-xvarphi(n)/n$, where $varphi(x, n)$ is the Legendre totient function and $varphi(n)$ is the Euler totient function. An inequality for $Delta(x, n)$ is known. In this paper we give a unitary analogue of this inequality, and more generally we give this inequality in the setting of regular convolutions.

         
       
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