Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:31:23.635323Z
Paper Citation Record · LEDGER
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences
As of 16 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:1908.05123.
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 2026-08-16T06:30:59.297886+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
18 of 18 outbound references displayed
- verified exact1
- verified fuzzy14
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation ee4e74a4-0226-48e5-ade0-dce0f7997101 · outbound
This paper cites Almkvist and J.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Almkvist and J
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:24.024721Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b7a50841-5c14-4b9b-91cf-d4173f67b606 · outbound
This paper cites Baruah, B.C.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Baruah, B.C
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:24.004183Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 010777c3-1176-413d-a4f6-df27a0e44efa · outbound
This paper cites Chisholm, A.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Chisholm, A
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.983025Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8a6b7a8a-7cac-4567-bf00-702f72782a0a · outbound
This paper cites Special hypergeometric motives and their $L$-functions: Asai recognition.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Special hypergeometric motives and their $L$-functions: Asai recognition
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T13:31:23.691359Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 67340b4c-3f64-46a8-a684-4d4144368cc8 · outbound
This paper cites Guillera , A matrix form of Ramanujan-type series for 1 /π , Gems in Experimental Mathematics: Contemp.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Guillera , A matrix form of Ramanujan-type series for 1 /π , Gems in Experimental Mathematics: Contemp
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.965930Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9e97abe8-dec5-4131-b917-d54f06bb429f · outbound
This paper cites Guillera , More hypergeometric identities related to Ramanujan-type serie s, The Ramanujan J.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Guillera , More hypergeometric identities related to Ramanujan-type serie s, The Ramanujan J
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.946753Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8a296d9a-e12c-4bfb-b626-fd8a0c754fce · outbound
This paper cites Guillera , WZ pairs and q-analogues of Ramanujan series for 1 /π (with an appendix by Wadim Zudilin), Journal of Difference Equations and Applications 24, 1871– 1879.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Guillera , WZ pairs and q-analogues of Ramanujan series for 1 /π (with an appendix by Wadim Zudilin), Journal of Difference Equations and Applications 24, 1871– 1879
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.927689Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 06484bc5-ad7e-42d3-affd-32fdc8d8b602 · outbound
This paper cites Divergent.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Divergent
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.903448Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 66d0f2cc-9eea-4817-b332-4f4a14f8b2fa · outbound
This paper cites an unresolved cited work.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:31:23.884624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 62d06fc7-b7cc-41b6-8524-f30222bc898e · outbound
This paper cites Long , Hypergeoemetric evaluation identities and supercongruences, P acific Journal of Mathe- matics 249 (2011), 405–418.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Long , Hypergeoemetric evaluation identities and supercongruences, P acific Journal of Mathe- matics 249 (2011), 405–418
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.865646Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2673b4cf-4cd5-4f6c-9598-b8cf3444080c · outbound
This paper cites Morley , Note on the congruence 2 4n ≡ (−1)n(2n)!/ (n!)2, where 2 n + 1 is prime, Ann.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Morley , Note on the congruence 2 4n ≡ (−1)n(2n)!/ (n!)2, where 2 n + 1 is prime, Ann
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.848224Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 76574214-5b53-4bb9-ad7f-8360e3a8ac27 · outbound
This paper cites Petkov˘sek, H.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Petkov˘sek, H
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.830919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a8cf0c3e-5fad-4ebc-adef-f9e1c6ae947d · outbound
This paper cites Wolstenholme , On certain properties of prime numbers, Quart.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Wolstenholme , On certain properties of prime numbers, Quart
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.813306Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0bda36dd-35aa-4461-be73-31b33eecc041 · outbound
This paper cites an unresolved cited work.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:31:23.792529Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a3d30175-9452-4838-bbc2-12f5a3cbd148 · outbound
This paper cites an unresolved cited work.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:31:23.772598Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 51d4632d-e03b-4341-be3a-98f1916cdbc3 · outbound
This paper cites Zudilin , Ramanujan-type formulae for 1 /π : A second wind? in Modular Forms and String Duality (Banff, June 3–8, 2006), N.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Zudilin , Ramanujan-type formulae for 1 /π : A second wind? in Modular Forms and String Duality (Banff, June 3–8, 2006), N
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.752086Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0b8003e8-4cdf-44c4-8acb-14eb1a678c1d · outbound
This paper cites Zudilin , Ramanujan-type supercongruences, J.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Zudilin , Ramanujan-type supercongruences, J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.731159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3ebeb59b-99ee-40fe-93bf-a48a07caa504 · outbound
This paper cites Zudilin , Arithmetic hypergeometric series, Russian Math.
Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences Zudilin , Arithmetic hypergeometric series, Russian Math
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:31:23.711612Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.