On the iterates of Euler's function |
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| Authors: | R. Warlimont |
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| Affiliation: | The John Knopfmacher Centre for, Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg 2050, South Africa, ZA
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| Abstract: | Asymptotic representations are given for the three sums ?n ￡ x j(n)/j(j(n))textstylesumlimits limits _{nle x} varphi (n)/varphi bigl (varphi (n)bigr ), ?n ￡ x j(n)/j(j(n))textstylesumlimits limits _{nle x} varphi (n)/varphi bigl (varphi (n)bigr ), ?n ￡ x log j(n)/j(j(n)) ; jtextstylesumlimits limits _{nle x} log , varphi (n)/varphi bigl (varphi (n)bigr ) ; varphi is Euler's function. |
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