Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-24T07:21:33.729754Z
Paper Citation Record · LEDGER
Real exponential sums over primes and prime gaps
As of 12 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2307.08725.
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
19 of 19 outbound references displayed
- verified exact0
- verified fuzzy13
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 94895c4b-cd2b-4438-b439-74b2856b02ca · outbound
This paper cites Algorithmic Number Theory, Volume 1: Efficient Algorithms.
Real exponential sums over primes and prime gaps Algorithmic Number Theory, Volume 1: Efficient Algorithms
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.334776Z
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 c0108168-2921-4cdc-816c-0819a7f70777 · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.328417Z
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 2ab62f67-9634-4838-a529-bd2c16c22b45 · outbound
This paper cites Erd˝ os.Beweis eines Satzes von Tschebyschef.
Real exponential sums over primes and prime gaps Erd˝ os.Beweis eines Satzes von Tschebyschef
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.325345Z
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 0338fa19-3f05-4cac-b222-b4e7491b9812 · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.321877Z
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 891fdf87-f2b0-4a0c-b47f-eb484c9105b8 · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.331354Z
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 7ba5b9a4-a938-4a87-b4ad-f5d82c1046ae · outbound
This paper cites Introduction to Number Theory.
Real exponential sums over primes and prime gaps Introduction to Number Theory
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.318329Z
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 8a5c06a7-e803-4e72-b7bc-7ff77dd46e2d · outbound
This paper cites Abstract Analytic Number Theory.
Real exponential sums over primes and prime gaps Abstract Analytic Number Theory
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.338573Z
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 0d1aa1ae-1c68-4a44-ac1e-d322cdbb60fc · outbound
This paper cites Analytic Number Theory - Exploring the Anatomy of the Intege rs.
Real exponential sums over primes and prime gaps Analytic Number Theory - Exploring the Anatomy of the Intege rs
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.366480Z
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 7222a8dc-1918-4905-baa7-d1f22803ee31 · outbound
This paper cites Complex Analysis.
Real exponential sums over primes and prime gaps Complex Analysis
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.369782Z
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 64ccfb24-6eb1-4d72-95e9-8691fa9f50d4 · outbound
This paper cites Primes in short intervals.
Real exponential sums over primes and prime gaps Primes in short intervals
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.373566Z
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 447d7ca9-03d8-46cd-bc92-f8cf427fb642 · outbound
This paper cites Montgomery.
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.376956Z
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 0bcb76b2-125a-45b6-a284-cd207814de82 · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.380373Z
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 df9ccda8-2b3f-4677-be5e-5fd33421468c · outbound
This paper cites The prime number theorem: Analytic and elementary proofs.
Real exponential sums over primes and prime gaps The prime number theorem: Analytic and elementary proofs
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.356604Z
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 42b3a14f-f771-494e-a9de-5540deeecd03 · outbound
This paper cites N´ umeros primos: mist´ erios e recordes.
Real exponential sums over primes and prime gaps N´ umeros primos: mist´ erios e recordes
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.363079Z
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 19b15ee4-07e4-467d-a447-c2d17a017c11 · outbound
This paper cites Barkley Rosser; Lowell Schoenfeld.
Real exponential sums over primes and prime gaps Barkley Rosser; Lowell Schoenfeld
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.349295Z
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 542de187-a94d-44c0-9d57-9d6392e0f423 · outbound
This paper cites Acta Fac.
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.341985Z
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 829773d6-93a0-4e61-afcb-32e1b6e97d07 · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.345693Z
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 28db9b23-cfb6-4c4b-8a0a-8a7650c4b2a3 · outbound
This paper cites Sutherland.
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T07:24:07.353266Z
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 894bd225-14df-4ee3-93b8-16b8f4ff656c · outbound
This paper cites an unresolved cited work.
Real exponential sums over primes and prime gaps Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T07:24:07.359743Z
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.