Oscillations of the remainder term related to the Euler totient function |
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Authors: | Jerzy Kaczorowski Kazimierz Wiertelak |
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Affiliation: | Adam Mickiewicz University, Faculty of Mathematics and Computer Science, 61-614 Poznań, Poland |
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Abstract: | We split the remainder term in the asymptotic formula for the mean of the Euler phi function into two summands called the arithmetic and the analytic part respectively. We show that the arithmetic part can be studied with a mild use of the complex analytic tools, whereas the study of the analytic part heavily depends on the properties of the Riemann zeta function and on the distribution of its non-trivial zeros in particular. |
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Keywords: | Euler totient function Omega theorems Riemann Hypothesis Oscillations of the remainder term |
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