\'Etude statistique du facteur premier m\'edian, 4: somme des inverses
Jonathan Rotg\'e
TL;DR
This paper investigates the sum of reciprocals of the middle prime factor of integers, providing new asymptotic formulas that improve upon previous estimates in the literature.
Contribution
It introduces novel asymptotic expansions and formulas for the sum of reciprocals of the middle prime factor, considering multiplicity and non-multiplicity cases.
Findings
Asymptotic expansion for the case with multiplicity
Asymptotic formula involving an implicit parameter for the non-multiplicity case
Improves accuracy of previous estimates
Abstract
We consider the sum of the reciprocals of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an asymptotic expansion in the first case and an asymptotic formula involving an implicit parameter in the second. Both these results improve on previous estimates available in the literature.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.