Nous étudions le logarithme du plus petit commun multiple de la séquence de nombres entiers . En utilisant un résultat de Homma [5] sur la distribution des racines de polynômes quadratiques modulo des nombres premiers, nous calculons le terme d’erreur dans les formules obtenues par Cilleruelo [3].
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [5] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [3].
@article{JTNB_2013__25_2_457_0,
author = {Ru\'e, Juanjo and \v{S}arka, Paulius and Zumalac\'arregui, Ana},
title = {On the error term of the logarithm of the lcm of a quadratic sequence},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {457--470},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {25},
number = {2},
year = {2013},
doi = {10.5802/jtnb.843},
zbl = {1283.11058},
mrnumber = {3228315},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.843/}
}
TY - JOUR AU - Rué, Juanjo AU - Šarka, Paulius AU - Zumalacárregui, Ana TI - On the error term of the logarithm of the lcm of a quadratic sequence JO - Journal de théorie des nombres de Bordeaux PY - 2013 SP - 457 EP - 470 VL - 25 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.843/ DO - 10.5802/jtnb.843 LA - en ID - JTNB_2013__25_2_457_0 ER -
%0 Journal Article %A Rué, Juanjo %A Šarka, Paulius %A Zumalacárregui, Ana %T On the error term of the logarithm of the lcm of a quadratic sequence %J Journal de théorie des nombres de Bordeaux %D 2013 %P 457-470 %V 25 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.843/ %R 10.5802/jtnb.843 %G en %F JTNB_2013__25_2_457_0
Rué, Juanjo; Šarka, Paulius; Zumalacárregui, Ana. On the error term of the logarithm of the lcm of a quadratic sequence. Journal de théorie des nombres de Bordeaux, Tome 25 (2013) no. 2, pp. 457-470. doi : 10.5802/jtnb.843. http://www.numdam.org/articles/10.5802/jtnb.843/
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