Geodesic
On the first sign change in Mertens' theorem
Jan B\"uthe1
1 Hausdorff Center for Mathematics Endenicher Allee 62 53115 Bonn, Germany
Acta Arithmetica, Tome 171 (2015) no. 2, pp. 183-195.

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

The function $\sum_{p\leq x} 1/p - \log\log(x) - M$ is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before $\exp(495.702833165)$.
DOI : 10.4064/aa171-2-5
Keywords: function sum leq log log known change sign infinitely often far calculated values positive paper prove first sign change occurs before exp

Jan B\"uthe 1

1 Hausdorff Center for Mathematics Endenicher Allee 62 53115 Bonn, Germany 
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Jan B\"uthe. On the first sign change in Mertens' theorem. Acta Arithmetica, Tome 171 (2015) no. 2, pp. 183-195. doi : 10.4064/aa171-2-5. http://geodesic.mathdoc.fr/articles/10.4064/aa171-2-5/

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