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

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.

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.

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DOI : 10.5802/jtnb.1163
Classification : 11N25, 11N37, 11N56, 11N60, 11N64, 11N69, 11B25, 11B83
Mots clés : $k$-free number, variance, arithmetic progression
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 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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