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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Mots clés : $k$-free number, variance, arithmetic progression
@article{JTNB_2021__33_2_317_0,
author = {Parry, Tomos},
title = {A variance for $k$-free numbers in arithmetic progressions of given modulus},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {317--360},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {33},
number = {2},
year = {2021},
doi = {10.5802/jtnb.1163},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.1163/}
}
TY - JOUR AU - Parry, Tomos TI - A variance for $k$-free numbers in arithmetic progressions of given modulus JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 317 EP - 360 VL - 33 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1163/ DO - 10.5802/jtnb.1163 LA - en ID - JTNB_2021__33_2_317_0 ER -
%0 Journal Article %A Parry, Tomos %T A variance for $k$-free numbers in arithmetic progressions of given modulus %J Journal de théorie des nombres de Bordeaux %D 2021 %P 317-360 %V 33 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.1163/ %R 10.5802/jtnb.1163 %G en %F JTNB_2021__33_2_317_0
Parry, Tomos. 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. http://www.numdam.org/articles/10.5802/jtnb.1163/
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