Geodesic
On some arithmetical functions and the number of pure number fields
Yusuke Fujisawa1
1 Seiwa Inc. 28-13 Hataya 2-chome Atsuta-ku, Nagoya, Japan
Colloquium Mathematicum, Tome 149 (2017) no. 2, pp. 275-290.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

First, we define the Möbius and Liouville functions of order $k$ over a number field $F$ for a positive integer $k$. We give formulas for their partial sums. Moreover, we consider the number of $k$-free ideals of the integer ring of $F$. Next, we investigate the number of pure number fields. In the previous paper, we considered lower and upper bounds of that number. However, the estimates were too coarse. One of the purposes of this paper is to improve the upper bound.
DOI : 10.4064/cm6970-12-2016
Keywords: first define bius liouville functions order number field positive integer formulas their partial sums moreover consider number k free ideals integer ring investigate number pure number fields previous paper considered lower upper bounds number however estimates too coarse purposes paper improve upper bound

Yusuke Fujisawa 1

1 Seiwa Inc. 28-13 Hataya 2-chome Atsuta-ku, Nagoya, Japan 
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Yusuke Fujisawa. On some arithmetical functions and the number of pure number fields. Colloquium Mathematicum, Tome 149 (2017) no. 2, pp. 275-290. doi : 10.4064/cm6970-12-2016. http://geodesic.mathdoc.fr/articles/10.4064/cm6970-12-2016/

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