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- W2973722608 abstract "The Jordan totient Jk(n) can be defined by Jk(n)=nk∏p|n(1−p−k). In this paper, we study the average behavior of fractions P/Q of two products P and Q of Jordan totients, which we call Jordan totient quotients. To this end, we describe two general and ready-to-use methods that allow one to deal with a larger class of totient functions. The first one is elementary and the second one uses an advanced method due to Balakrishnan and Pétermann. As an application, we determine the average behavior of the Jordan totient quotient, the kth normalized derivative of the nth cyclotomic polynomial Φn(z) at z=1, the second normalized derivative of the nth cyclotomic polynomial Φn(z) at z=−1, and the average order of the Schwarzian derivative of Φn(z) at z=1." @default.
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- W2973722608 date "2020-04-01" @default.
- W2973722608 modified "2023-10-05" @default.
- W2973722608 title "Jordan totient quotients" @default.
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- W2973722608 doi "https://doi.org/10.1016/j.jnt.2019.08.014" @default.
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