Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:33:46.458758Z
Paper Citation Record · LEDGER
On the connection between zero-free regions and the error term in the Prime Number Theorem
As of 12 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.13780.
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 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
25 of 25 outbound references displayed
- verified exact2
- verified fuzzy11
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 2518a2d3-51ec-4b07-8dc6-83bf8229f23a · outbound
This paper cites Explicit zero density estimate near unity.
On the connection between zero-free regions and the error term in the Prime Number Theorem Explicit zero density estimate near unity
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:33:47.051290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b4b8118d-abe0-4ee8-812a-8a0eb99cb8dd · outbound
This paper cites Bellotti, Explicit bounds for the Riemann zeta function and a new zero-free region , J.
On the connection between zero-free regions and the error term in the Prime Number Theorem Bellotti, Explicit bounds for the Riemann zeta function and a new zero-free region , J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:52.213783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 3990d55a-cb93-485a-962e-448e27c48a88 · outbound
This paper cites Beurling, Analyse de la loi asymptotique de la distribution des nombres premiers g´ en´ eralis´ es.
On the connection between zero-free regions and the error term in the Prime Number Theorem Beurling, Analyse de la loi asymptotique de la distribution des nombres premiers g´ en´ eralis´ es
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:52.057881Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5bd42c3e-2000-4fd5-9148-43b88e933e5f · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:51.907166Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c20342c5-66cd-4bd5-b4e4-e99c2857b89a · outbound
This paper cites Broucke, On zero-density estimates for Beurling zeta functions , to appear in Ann.
On the connection between zero-free regions and the error term in the Prime Number Theorem Broucke, On zero-density estimates for Beurling zeta functions , to appear in Ann
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:51.808003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2262ade7-6f53-429d-bca0-92ec9c469ca7 · outbound
This paper cites Broucke, G.
On the connection between zero-free regions and the error term in the Prime Number Theorem Broucke, G
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:51.604801Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8c8de14d-6cff-492a-94c7-e543fca99907 · outbound
This paper cites Broucke, J.
On the connection between zero-free regions and the error term in the Prime Number Theorem Broucke, J
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:51.345652Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation bdb9f4ef-cbbf-4b66-a73f-08377c10171d · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:51.048380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 48d64cba-2e4b-4d68-9e17-d454d43612dc · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:50.765333Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a811c6a8-c008-4a4b-898e-40c31be8b901 · outbound
This paper cites Hal´ asz, P.
On the connection between zero-free regions and the error term in the Prime Number Theorem Hal´ asz, P
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:50.473369Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c7762474-d63b-45cc-9066-67d52aa346ee · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:50.145043Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9636e8bc-2a09-4446-af35-cd7fea742f9a · outbound
This paper cites Ivi´ c,The Riemann Zeta-Function.
On the connection between zero-free regions and the error term in the Prime Number Theorem Ivi´ c,The Riemann Zeta-Function
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:49.855026Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 75eb2c65-39a2-4115-a9f5-8bd78f2a6aae · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 13
- Resolution
- verified exact
- raw_fallback, observed 2026-08-06T16:33:46.863911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4ba71c85-472b-444b-8e54-354f5195fbc9 · outbound
This paper cites Landau, Handbuch der Lehre von der Verteilung der Primzahlen , Teubner, Leipzig–Berlin, 1909.
On the connection between zero-free regions and the error term in the Prime Number Theorem Landau, Handbuch der Lehre von der Verteilung der Primzahlen , Teubner, Leipzig–Berlin, 1909
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:49.490610Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 34ec60a2-2ec6-46df-abc6-c3393abd6b24 · outbound
This paper cites Landau, ¨Uber die Wurzeln der Zetafunktion , Math.
On the connection between zero-free regions and the error term in the Prime Number Theorem Landau, ¨Uber die Wurzeln der Zetafunktion , Math
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:49.218613Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f3660375-d0b5-44d7-8208-33c08fd761fc · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:49.017081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d77881db-e4e0-4ed3-a2e1-f6c759cbd258 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:48.698833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8b0f8a19-6816-490f-bdef-941f46b13fff · outbound
This paper cites Pintz, On the remainder term of the prime number formula II.
On the connection between zero-free regions and the error term in the Prime Number Theorem Pintz, On the remainder term of the prime number formula II
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:48.493833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 69007685-8df8-4a2e-99e1-82a827ba2ea4 · outbound
This paper cites Pintz, On the density theorem of Hal´ asz and Tur´ an, Acta Math.
On the connection between zero-free regions and the error term in the Prime Number Theorem Pintz, On the density theorem of Hal´ asz and Tur´ an, Acta Math
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:33:48.306045Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 04b27e39-c32e-4a86-9166-f2df3acf81f9 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:48.142371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 325e750c-f2cf-45c4-86dd-eba28f4179f4 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:47.958585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5740e5b6-14ca-4527-a62b-e1480c220b5d · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:47.782981Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c94de6ee-fe58-466e-a2e1-92afc45f9d21 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 23
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:33:46.209810Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d40d39d0-a420-41fa-9e65-e46c69154e96 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:47.495465Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 91d1ecbd-6b6e-4e3d-8a34-d8ee11f09ce5 · outbound
This paper cites an unresolved cited work.
On the connection between zero-free regions and the error term in the Prime Number Theorem Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:33:47.278625Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
No inbound Pith citation observations are available.