English

Remainder in Modified Mertens Formula and Ramanujan Inequality

Number Theory 2022-01-11 v1

Abstract

A highly strong upper estimate in the modified asymptotic formula for sums of the primes' reciprocals is proved to be necessary (as well as sufficient) in order the Ramanujan inequality holds true. Some other criteria in similar terms are also obtained.

Keywords

Cite

@article{arxiv.2201.02663,
  title  = {Remainder in Modified Mertens Formula and Ramanujan Inequality},
  author = {Gennadiy Kalyabin},
  journal= {arXiv preprint arXiv:2201.02663},
  year   = {2022}
}

Comments

9 pages, 9 references

R2 v1 2026-06-24T08:43:17.898Z