On the error term of the logarithm of the lcm of a quadratic sequence
Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 457-470.

We study the logarithm of the least common multiple of the sequence of integers given by 1 2 +1,2 2 +1,,n 2 +1. 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].

Nous étudions le logarithme du plus petit commun multiple de la séquence de nombres entiers 1 2 +1,2 2 +1,,n 2 +1. 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].

Published online:
DOI: 10.5802/jtnb.843
Juanjo Rué 1; Paulius Šarka 2; Ana Zumalacárregui 3

1 Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) Nicolás Cabrera 13-15 28049 Madrid, Spain
2 Institute of Mathematics and Informatics Akademijos 4 08663 Vilnius, Lithuania and Department of Mathematics and Informatics, Vilnius University Naugarduko 24 03225 Vilnius, Lithuania
3 Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departmento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain
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Juanjo Rué; Paulius Šarka; Ana Zumalacárregui. On the error term of the logarithm of the lcm of a quadratic sequence. Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 457-470. doi : 10.5802/jtnb.843. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.843/

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