Abstract
It is proved in [1] that the error term associated with the summatory function of the divisor function σ−1 (n) satisfies (1)E −1 (loglogx) with an implied constantC −≥(e γ−1)/2. In fact, the method of [1] yields the better (2)C −≥e γ/2, and also (3)E −1 (log logx) with an implied constant (4)C +≥e γ/2.
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Reference
An Ω-theorem for an error term related to the sum-of-divisors function. Mh. Math.103, 145–157 (1987).
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Pétermann, Y.F.S. An Ω-theorem...: Addendum. Monatshefte für Mathematik 105, 193–194 (1988). https://doi.org/10.1007/BF01636927
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DOI: https://doi.org/10.1007/BF01636927