English

Generalized Mertens sums

Number Theory 2019-10-08 v1

Abstract

Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.

Keywords

Cite

@article{arxiv.1910.02781,
  title  = {Generalized Mertens sums},
  author = {Gérald Tenenbaum},
  journal= {arXiv preprint arXiv:1910.02781},
  year   = {2019}
}

Comments

After seeing a recent preprint of Tianfang Qi and Su Hu (arXiv:1909.10930) on the same subject, but using a different approach, an minor overlook with respect to the published version has been corrected

R2 v1 2026-06-23T11:36:22.557Z