A variance for k-free numbers in arithmetic progressions of given modulus
Journal de Théorie des Nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 317-360.

An asymptotic formula for the variance of squarefree numbers in arithmetic progressions of given modulus was obtained by Nunes, see [9]. We improve one of the error terms as far as one would expect to be able to go.

Une formule asymptotique pour la variance des nombres entiers sans facteur carré dans une progression arithmétique de raison donnée a été trouvée par Nunes dans [9]. Pour l’un des termes d’erreur, nous donnons la meilleure amélioration que l’on puisse espérer d’avoir.

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Accepted:
Published online:
DOI: 10.5802/jtnb.1163
Classification: 11N25,  11N37,  11N56,  11N60,  11N64,  11N69,  11B25,  11B83
Keywords: k-free number, variance, arithmetic progression
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Tomos Parry. A variance for $k$-free numbers in arithmetic progressions of given modulus. Journal de Théorie des Nombres de Bordeaux, Volume 33 (2021) no. 2, pp. 317-360. doi : 10.5802/jtnb.1163. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1163/

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