Pith. sign in

REVIEW 1 cited by

Sign changes in Mertens' first and second theorems

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1505.03589 v1 pith:WJ6NUZAE submitted 2015-05-14 math.NT

classification math.NT
keywords mertenssignaffirmativeanswersassumptionsbiasbuildcertain
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We show that the functions $\sum_{p\leq x} (\log p)/p - \log x - E$ and $\sum_{p\leq x} 1/p - \log \log x -B$ change sign infinitely often, and that under certain assumptions, they exhibit a strong bias towards positive values. These results build on recent work of Diamond & Pintz and Lamzouri concerning oscillation of Mertens' product formula, and answers to the affirmative a question posed by Rosser and Schoenfeld.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Correlations of error terms for weighted prime counting functions

    math.NT 2025-07 unverdicted novelty 7.0 of 10

    The paper proves equivalences between the Riemann hypothesis and persistent inequalities of normalized error terms in weighted prime counting functions, and computes conditional logarithmic densities of sign agreement...

Pith tools