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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_aa171_2_5,
     author = {Jan B\"uthe},
     title = {On the first sign change in {Mertens'} theorem},
     journal = {Acta Arithmetica},
     pages = {183--195},
     year = {2015},
     volume = {171},
     number = {2},
     doi = {10.4064/aa171-2-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa171-2-5/}
}
TY  - JOUR
AU  - Jan B\"uthe
TI  - On the first sign change in Mertens' theorem
JO  - Acta Arithmetica
PY  - 2015
SP  - 183
EP  - 195
VL  - 171
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa171-2-5/
DO  - 10.4064/aa171-2-5
LA  - en
ID  - 10_4064_aa171_2_5
ER  - 
%0 Journal Article
%A Jan B\"uthe
%T On the first sign change in Mertens' theorem
%J Acta Arithmetica
%D 2015
%P 183-195
%V 171
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/aa171-2-5/
%R 10.4064/aa171-2-5
%G en
%F 10_4064_aa171_2_5
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

Cité par Sources :