On the first sign change in Mertens' theorem

Jan Büthe. "On the first sign change in Mertens' theorem." Acta Arithmetica 171.2 (2015): 183-195. <http://eudml.org/doc/279366>.

@article{JanBüthe2015,
abstract = {The function $∑_\{p≤x\} 1/p - loglog(x) - M$ 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).},
author = {Jan Büthe},
journal = {Acta Arithmetica},
keywords = {Mertens' theorem; sign changes; Skewes number},
language = {eng},
number = {2},
pages = {183-195},
title = {On the first sign change in Mertens' theorem},
url = {http://eudml.org/doc/279366},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Jan Büthe
TI - On the first sign change in Mertens' theorem
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 2
SP - 183
EP - 195
AB - The function $∑_{p≤x} 1/p - loglog(x) - M$ 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).
LA - eng
KW - Mertens' theorem; sign changes; Skewes number
UR - http://eudml.org/doc/279366
ER -