Geodesic
Omega results for the error term in the square-free divisor problem for square-full integers
Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 1011-1028

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DOI

In this paper, we investigate the distributive properties of square-free divisors over square-full integers. We first compute the mean value of the number of such divisors and obtain the error term which appears in its asymptotic formula. We then show that if one assumes the Riemann Hypothesis, then the omega estimate of such an error term can be drastically improved. Finally, we compute the omega estimate of the mean square of such an error term.
DOI : 10.4153/S0008439524000225
Mots-clés : Divisor function, Riemann zeta function, zero-free region, zero density estimates, Riemann Hypothesis 
Banerjee, Debika; Minamide, Makoto T. Omega results for the error term in the square-free divisor problem for square-full integers. Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 1011-1028. doi: 10.4153/S0008439524000225
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     title = {Omega results for the error term in the square-free divisor problem for square-full integers},
     journal = {Canadian mathematical bulletin},
     pages = {1011--1028},
     year = {2024},
     volume = {67},
     number = {4},
     doi = {10.4153/S0008439524000225},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000225/}
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