Abstract
Let θ(x) = ∑_{p≤x}log_{p}. We show that θ(x) < x for 2 < x < 1.39·1017. We
also show that there is an x < exp(727.951332668) for which θ(x) > x.
Original language  English 

Pages (fromto)  15391547 
Number of pages  9 
Journal  Mathematics of Computation 
Volume  85 
DOIs  
Publication status  Published  21 Aug 2015 
Keywords
 Sign changes of arithmetical functions
 oscillation theorems
Equipment

HPC (High Performance Computing) Facility
Sadaf R Alam (Manager), Steven A Chapman (Manager), Polly E Eccleston (Other), Simon H Atack (Other) & D A G Williams (Manager)
Facility/equipment: Facility