Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T12:52:42.415157Z
Paper Citation Record · LEDGER
On the number of exceptional intervals to the prime number theorem in short intervals
As of 18 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2505.24017.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-27T20:49:36.275111Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-02T20:17:21.306242Z
Reference resolution
38 of 38 outbound references displayed
- verified exact1
- verified fuzzy21
- unresolved16
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation ce7c0d9f-8f5a-4d36-b096-5802c4f524ca · outbound
This paper cites Bourgain,On the distribution of Dirichlet sums.
On the number of exceptional intervals to the prime number theorem in short intervals Bourgain,On the distribution of Dirichlet sums
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:50.963413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a3da42fa-787c-49d3-8196-0a6e92d6ec36 · outbound
This paper cites Bourgain,On large values estimates for Dirichlet polynomials and the density hypothesis for the Riemann zeta function, Internat.
On the number of exceptional intervals to the prime number theorem in short intervals Bourgain,On large values estimates for Dirichlet polynomials and the density hypothesis for the Riemann zeta function, Internat
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:50.768275Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 468f4f4e-8c34-4850-9b4e-99e606f412ad · outbound
This paper cites Bazzanella,Primes in almost all short intervals, Boll.
On the number of exceptional intervals to the prime number theorem in short intervals Bazzanella,Primes in almost all short intervals, Boll
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:50.556874Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 225c32ba-b646-40d1-b1ae-7c24d2cf5f88 · outbound
This paper cites Bazzanella,Primes in almost all short intervals II, Boll.
On the number of exceptional intervals to the prime number theorem in short intervals Bazzanella,Primes in almost all short intervals II, Boll
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:50.405259Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f20b7b4e-a406-4024-be1b-5b62b8c9dabe · outbound
This paper cites Bazzanella,Two conditional results about primes in short intervals, Int.
On the number of exceptional intervals to the prime number theorem in short intervals Bazzanella,Two conditional results about primes in short intervals, Int
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:50.178707Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3f2181d8-57ee-4814-be53-361cb9593dee · outbound
This paper cites Bazzanella, A.
On the number of exceptional intervals to the prime number theorem in short intervals Bazzanella, A
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:52:38.688278Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59f66c01-66c5-43bb-a98f-45d469f71bc3 · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:50.009691Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9d960a5c-baa3-43fa-b9b3-393c1863687a · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:49.793277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a50f1bde-0bac-4d1a-a23c-5dc8654b7211 · outbound
This paper cites Cram´ er,On the order of magnitude of the difference between consecutive prime numbers, Acta Arith- metica2(1936), 23–46.
On the number of exceptional intervals to the prime number theorem in short intervals Cram´ er,On the order of magnitude of the difference between consecutive prime numbers, Acta Arith- metica2(1936), 23–46
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:49.605462Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d2b92647-3aea-467b-bb7e-7f11cc0c78e5 · outbound
This paper cites Davenport,Multiplicative number theory, 2nd ed., Springer-Verlag, New York/Berlin, 1980.
On the number of exceptional intervals to the prime number theorem in short intervals Davenport,Multiplicative number theory, 2nd ed., Springer-Verlag, New York/Berlin, 1980
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:49.376010Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 908fd40a-1abc-4541-9d73-0db533495f4b · outbound
This paper cites Ford,Vinogradov’s integral and bounds for the Riemann zeta function, Proc.
On the number of exceptional intervals to the prime number theorem in short intervals Ford,Vinogradov’s integral and bounds for the Riemann zeta function, Proc
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:49.147022Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 115381f4-fda2-4ddd-812b-800a35ce11f6 · outbound
This paper cites Hal´ asz, P.
On the number of exceptional intervals to the prime number theorem in short intervals Hal´ asz, P
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:48.959196Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fdd4c7a9-46eb-4d84-acd5-a60120dece23 · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:48.712623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 33b81523-c8bf-450e-a336-644517e3a2b3 · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:48.458767Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b7ceedc3-7520-410f-94b5-b7f4ea85cf54 · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:48.254908Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3c5201ce-7663-4075-ace1-337dd863eadf · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:48.041017Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bdb42b40-0c3e-4ed8-9e2e-eaf50046e62f · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:47.869258Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e21af74b-b579-4371-bd19-f4949436e7fc · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:47.592695Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 918ed49d-767f-4051-ab77-f229e53d586e · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:47.353787Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d58a61f8-da06-4982-be30-ac660608fa82 · outbound
This paper cites Islam,Multiplicative properties of integers in short intervals, PhD thesis, Royal Holloway, University of London, 2015.
On the number of exceptional intervals to the prime number theorem in short intervals Islam,Multiplicative properties of integers in short intervals, PhD thesis, Royal Holloway, University of London, 2015
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:47.082080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5f842741-1c65-4b9f-aebe-b7040a9ff6b3 · outbound
This paper cites Ivi´ c,On sums of large differences between consecutive primes, Math.
On the number of exceptional intervals to the prime number theorem in short intervals Ivi´ c,On sums of large differences between consecutive primes, Math
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:46.814891Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fe14f1d7-daa4-4cc9-8d78-b2cb05f540cc · outbound
This paper cites Ivi´ c,Exponent pairs and the zeta function of Riemann, Studia Sci.
On the number of exceptional intervals to the prime number theorem in short intervals Ivi´ c,Exponent pairs and the zeta function of Riemann, Studia Sci
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:46.493533Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3e819439-211d-417c-bdac-421fe246561a · outbound
This paper cites Iwaniec, E.
On the number of exceptional intervals to the prime number theorem in short intervals Iwaniec, E
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:46.163455Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2fb7f764-7c3a-4e77-b6e6-1891f2ef1f08 · outbound
This paper cites On large differences between consecutive primes.
On the number of exceptional intervals to the prime number theorem in short intervals On large differences between consecutive primes
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:52:40.597399Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4465cf67-6a34-4107-918e-57eeaca030e2 · outbound
This paper cites Jutila,Zero-density estimates for L-functions, Acta Arithmetica32(1977), 52–62.
On the number of exceptional intervals to the prime number theorem in short intervals Jutila,Zero-density estimates for L-functions, Acta Arithmetica32(1977), 52–62
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:45.916911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 908eddd0-8d56-4a4c-b650-aa60864f35e3 · outbound
This paper cites Li,Primes in almost all short intervals, arXiv:2407.05651 [math.NT] (2024).
On the number of exceptional intervals to the prime number theorem in short intervals Li,Primes in almost all short intervals, arXiv:2407.05651 [math.NT] (2024)
Reference 27
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T12:52:42.843827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0f8fdf4e-ebd2-42a7-a72e-5722468acc08 · outbound
This paper cites Maier,Primes in short intervals, Michigan Math.
On the number of exceptional intervals to the prime number theorem in short intervals Maier,Primes in short intervals, Michigan Math
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:45.677626Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 041fd862-d186-482e-8027-4274da281f5b · outbound
This paper cites Matom¨ aki,Large differences between consecutive primes, The Quarterly Journal of Mathematics58 (2007), 489–518.
On the number of exceptional intervals to the prime number theorem in short intervals Matom¨ aki,Large differences between consecutive primes, The Quarterly Journal of Mathematics58 (2007), 489–518
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:45.413927Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation def2fa23-b90c-48ab-963d-e7d9fa4679fe · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:45.186088Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 541817cc-2357-4132-8b49-1d0af8fbbf5f · outbound
This paper cites Pintz,Density theorems for Riemann ’s zeta-function near the line, Acta Arithmetica208(2023), 1–13.
On the number of exceptional intervals to the prime number theorem in short intervals Pintz,Density theorems for Riemann ’s zeta-function near the line, Acta Arithmetica208(2023), 1–13
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:44.883866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 796d3a0e-39c6-4053-aa1c-00f5b1b04243 · outbound
This paper cites Selberg,On the normal density of primes in small intervals, and the difference between consecutive primes, Arch.
On the number of exceptional intervals to the prime number theorem in short intervals Selberg,On the normal density of primes in small intervals, and the difference between consecutive primes, Arch
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:44.583880Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a9055689-232f-4b74-af89-915800ae8af2 · outbound
This paper cites On the mean square gap between primes.
On the number of exceptional intervals to the prime number theorem in short intervals On the mean square gap between primes
Reference 33
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:52:41.620716Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a1cb09d9-ccbd-43e2-9746-76d0e7ae8b5a · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:44.306041Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dc7b5eb5-7b9a-4fc7-81e3-58803ffab1f0 · outbound
This paper cites New large value estimates for Dirichlet polynomials.
On the number of exceptional intervals to the prime number theorem in short intervals New large value estimates for Dirichlet polynomials
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:52:41.863810Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b9fc73f1-c4f4-405e-828b-16e21e22bad6 · outbound
This paper cites an unresolved cited work.
On the number of exceptional intervals to the prime number theorem in short intervals Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:52:44.019854Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation eba32a14-89f0-4f00-ad3a-334cb452554d · outbound
This paper cites Tur´ an,On a new method of analysis and its applications, Wiley-Interscience, New York, 1984.
On the number of exceptional intervals to the prime number theorem in short intervals Tur´ an,On a new method of analysis and its applications, Wiley-Interscience, New York, 1984
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:43.732003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 33cf0e9b-b146-4feb-99c6-f9e3948bb2fa · outbound
This paper cites Wolke,Grosse Differenzen zwischen aufeinanderfolgenden Primzahlen, Math.
On the number of exceptional intervals to the prime number theorem in short intervals Wolke,Grosse Differenzen zwischen aufeinanderfolgenden Primzahlen, Math
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:43.434548Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b0b5dcb9-b7cf-4cdf-ab7b-33a62c21275c · outbound
This paper cites Yu,The differences between consecutive primes, Bull.
On the number of exceptional intervals to the prime number theorem in short intervals Yu,The differences between consecutive primes, Bull
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:52:43.186750Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
Observation b1b1fdf3-67c4-469a-9c9c-9248a838e992 · inbound
Products of consecutive integers with unusual anatomy cites this paper.
Products of consecutive integers with unusual anatomy On the number of exceptional intervals to the prime number theorem in short intervals
Reference 23
- Resolution
- verified exact
- arxiv_id, observed 2026-05-27T15:06:21.364444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f051d462-9f91-4876-b188-2311d58297e0 · inbound
Gaps in Multiplicative Sidon Sets II cites this paper.
Gaps in Multiplicative Sidon Sets II On the number of exceptional intervals to the prime number theorem in short intervals
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-07-02T20:17:21.307456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.