TY - JOUR
T1 - Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function
AU - Trudgian, Tim
PY - 2015/7/1
Y1 - 2015/7/1
N2 - The purpose of this article is consider |ζ′(σ +it)/ζ(σ + it)| and |ζ(σ +it)|-1 when σ is close to unity. We prove that |ζ′(σ + it)/ζ(σ + it)| ≤ 87 log t and |ζ(σ + it)|-1≤ 6.9 × 106 log t for σ ≥ 1-1/(8 log t) and t ≥ 45.
AB - The purpose of this article is consider |ζ′(σ +it)/ζ(σ + it)| and |ζ(σ +it)|-1 when σ is close to unity. We prove that |ζ′(σ + it)/ζ(σ + it)| ≤ 87 log t and |ζ(σ + it)|-1≤ 6.9 × 106 log t for σ ≥ 1-1/(8 log t) and t ≥ 45.
KW - Prime number theorem
KW - Riemann zeta-function
KW - Zero-free region
UR - http://www.scopus.com/inward/record.url?scp=84934276639&partnerID=8YFLogxK
U2 - 10.7169/facm/2015.52.2.5
DO - 10.7169/facm/2015.52.2.5
M3 - Article
SN - 0208-6573
VL - 52
SP - 253
EP - 261
JO - Functiones et Approximatio, Commentarii Mathematici
JF - Functiones et Approximatio, Commentarii Mathematici
IS - 2
ER -