### 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 |
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Pages (from-to) | 1539-1547 |

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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## Cite this

Platt, D. J., & Trudgian, T. (2015). On the first sign change of

*θ(x)*-*x*.*Mathematics of Computation*,*85*, 1539-1547. https://doi.org/10.1090/mcom/3021