REVIEW 1 cited by
On the mean square gap between primes
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
abstract
We prove that the average size of the squares of differences between consecutive primes less than $x$ is $O(x^{0.23+\varepsilon})$ for any fixed $\varepsilon>0$. This improves on a result of Peck, who gave bound $O(x^{0.25+\varepsilon})$ in the place of $O(x^{0.23+\varepsilon})$. Key ingredients are Harman's sieve, Heath-Brown's mean value theorem for sparse Dirichlet polynomials and Heath-Brown's $R^*$ bound.
Forward citations
Cited by 1 Pith paper
-
On the number of exceptional intervals to the prime number theorem in short intervals
An explicit formula expresses the exceptional-set exponent for the short-interval prime number theorem in terms of zero density estimates, yielding improved numerical bounds such as μ(17/30) ≤ 7/12.
Discussion (0). Continue with ORCID to comment.