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  Volume 5, Issue 3, Article 61
 
On the $\ell_p$ Norm of GCD and Related Matrices
    Authors: Pentti Haukkanen,  
    Keywords: GCD matrix, LCM matrix, Smith's determinant, $ell_p$ norm, $O$-estimate  
    Date Received: 12/03/04  
    Date Accepted: 06/04/04  
    Subject Codes:

11C20; 15A36; 11A25

  
    Editors: Jozsef Sandor,  
 
    Abstract:

We estimate the $ ell_p$ norm of the $ ntimes n$ matrix, whose $ ij$ entry is $ % (i, j)^{s}/[i, j]^{r}$, where $ r, sinmathbb{R}$, $ (i, j)$ is the greatest common divisor of $ i$ and $ j$ and $ [i, j]$ is the least common multiple of $ i$ and $ j$.

         
       
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