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
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HPC (High Performance Computing) Facility
Susan L Pywell (Manager), Simon A Burbidge (Other), Polly E Eccleston (Other) & Simon H Atack (Other)
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