Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-24T20:08:07.174172Z
Paper Citation Record · LEDGER
The Landau function and the Riemann Hypothesis
As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:1907.07664.
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
27 of 27 outbound references displayed
- verified exact1
- verified fuzzy17
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1c58a500-a87d-4d5f-b595-6f78db2cca50 · outbound
This paper cites Abramowitz and I.
The Landau function and the Riemann Hypothesis Abramowitz and I
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.576065Z
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 d49cd869-7236-4910-8a4f-9d6e995de82d · outbound
This paper cites New bounds for the sum of the first $n$ prime numbers.
The Landau function and the Riemann Hypothesis New bounds for the sum of the first $n$ prime numbers
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-05-24T20:09:52.804878Z
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 fe08be87-ce4f-426f-bd75-d0c40b525d81 · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.565497Z
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 29a70131-a61f-47b2-babf-04494b87f22c · outbound
This paper cites Broughan.
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.572534Z
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 f7e11a52-dbe9-4f46-b850-860968b1f451 · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.592831Z
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 5dc794c6-e81c-4132-b68a-4f203424e638 · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.562004Z
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 3ac8a79e-8b3e-44ca-abb7-338195a4dcfa · outbound
This paper cites Deléglise and J.-L.
The Landau function and the Riemann Hypothesis Deléglise and J.-L
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.555188Z
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 3e578629-6d12-447f-b651-bd35a7392f39 · outbound
This paper cites Maximal product of primes whose sum is bounded, Proc.
The Landau function and the Riemann Hypothesis Maximal product of primes whose sum is bounded, Proc
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.624933Z
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 4d7644c4-7b90-46bb-8f49-f37781682f6f · outbound
This paper cites On the Largest Pr oduct of Primes with bounded sums, J.
The Landau function and the Riemann Hypothesis On the Largest Pr oduct of Primes with bounded sums, J
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.606892Z
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 4cdb4749-e26b-4003-82c4-9480dd28a349 · outbound
This paper cites An arithmetic e quivalence to the Riemann hypothesis, J.
The Landau function and the Riemann Hypothesis An arithmetic e quivalence to the Riemann hypothesis, J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.582447Z
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 e422e23d-f6c9-437d-8d48-1381a1a4dcce · outbound
This paper cites Landau’s func- tion for one million billions, J.
The Landau function and the Riemann Hypothesis Landau’s func- tion for one million billions, J
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.579196Z
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 736dd493-3205-430b-8581-d990ad5c510a · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.569167Z
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 e3db40c3-8b8a-4fb1-b6a1-fbfea2509d0d · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.558514Z
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 6c896286-949c-45d8-8d51-034a5c78def1 · outbound
This paper cites Massias and G.
The Landau function and the Riemann Hypothesis Massias and G
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.551360Z
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 b0550571-0459-443b-a0b6-14fe6c7d2617 · outbound
This paper cites Massias, J.-L.
The Landau function and the Riemann Hypothesis Massias, J.-L
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.548089Z
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 b3ae1beb-10ea-4553-8b6b-6ddd7e8f4671 · outbound
This paper cites Majoration explicite de l’ordre maximum d’un élément du groupe symétrique, Ann.
The Landau function and the Riemann Hypothesis Majoration explicite de l’ordre maximum d’un élément du groupe symétrique, Ann
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.636239Z
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 fef8c7e1-69cd-4fb5-8eda-79d58a3f08d7 · outbound
This paper cites Effective bounds for the maximal order of an element in the symmetric group, Math.
The Landau function and the Riemann Hypothesis Effective bounds for the maximal order of an element in the symmetric group, Math
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.628875Z
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 507b5493-0a06-40d9-82dc-46222aad935c · outbound
This paper cites Miller, The Maximal Order of an Element of a Finite Sym metric Group.
The Landau function and the Riemann Hypothesis Miller, The Maximal Order of an Element of a Finite Sym metric Group
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.613917Z
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 01de8af0-2268-4469-aee8-822b681dff3b · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.603446Z
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 7f298dd3-f95d-4327-9adf-247e5dcd2497 · outbound
This paper cites Nicolas, On Landau’s function /u1D454( /u1D45B).
The Landau function and the Riemann Hypothesis Nicolas, On Landau’s function /u1D454( /u1D45B)
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.596284Z
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 925c3fd2-19de-4419-8cc5-5a52ebc2eb8c · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.599851Z
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 fc4d585d-5319-46b6-b2ba-fae8a976bb6b · outbound
This paper cites Ramanujan.
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.610139Z
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 8186d56c-69b9-4189-89c6-20c823730549 · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.621232Z
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 81122c57-690b-444b-9f05-41602ee9d72e · outbound
This paper cites Barkley Rosser and Lowell Schoenfeld, Approximate f ormulas for some functions of prime numbers, Illinois J.
The Landau function and the Riemann Hypothesis Barkley Rosser and Lowell Schoenfeld, Approximate f ormulas for some functions of prime numbers, Illinois J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.589643Z
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 0ca42774-ca36-4a15-9280-784e3d41bd17 · outbound
This paper cites an unresolved cited work.
The Landau function and the Riemann Hypothesis Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-05-24T20:09:53.617538Z
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 b9b1f973-1731-4b68-9c6a-613284d77804 · outbound
This paper cites Schoenfeld.
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.585779Z
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 7bc31ded-6c09-4568-abd5-97edc0445c2e · outbound
This paper cites Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208 Institut Camille Jordan, Mathématiques, Bât.
The Landau function and the Riemann Hypothesis Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208 Institut Camille Jordan, Mathématiques, Bât
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-24T20:09:53.632578Z
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.