Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T05:12:00.895263Z
Paper Citation Record · LEDGER
A $p$-Converse theorem for Real Quadratic Fields
As of 16 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2504.21799.
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
32 of 32 outbound references displayed
- verified exact2
- verified fuzzy9
- unresolved21
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation a8738514-1838-445c-a7ea-8f5bb574ca3a · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.244082Z
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 67af5119-85cc-487f-b3f9-9f16ab2c867f · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.234745Z
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 6dedc19c-63c5-46cc-a240-aa367ff6e187 · outbound
This paper cites Burungale, Christopher Skinner, and Ye Tian, The B irch and S winnerton- D yer conjecture: a brief survey , Nine mathematical challenges---an elucidation, Proc.
A $p$-Converse theorem for Real Quadratic Fields Burungale, Christopher Skinner, and Ye Tian, The B irch and S winnerton- D yer conjecture: a brief survey , Nine mathematical challenges---an elucidation, Proc
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.224120Z
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 a2992e4b-6584-4978-9e3c-60f9d9b2b0f0 · outbound
This paper cites Burungale and Ye Tian, p -converse to a theorem of G ross- Z agier, K olyvagin and R ubin , Invent.
A $p$-Converse theorem for Real Quadratic Fields Burungale and Ye Tian, p -converse to a theorem of G ross- Z agier, K olyvagin and R ubin , Invent
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.214119Z
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 667b2c1c-0355-45a7-bf80-3b4565671010 · outbound
This paper cites Exceptional zeros for Heegner points and $p$-converse to the theorem of Gross-Zagier and Kolyvagin.
A $p$-Converse theorem for Real Quadratic Fields Exceptional zeros for Heegner points and $p$-converse to the theorem of Gross-Zagier and Kolyvagin
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-16T05:12:00.961811Z
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 04432379-df7c-48b1-905f-931fe2d3b9eb · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.203714Z
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 f969a8be-e461-4bde-a4fb-0cb0e4539aad · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.193936Z
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 4944736f-a588-41ed-bb6e-c720a89f6723 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.183916Z
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 43320ee2-0386-4674-bd22-4acf3fabc732 · outbound
This paper cites Le Hung, and Samir Siksek, Elliptic curves over real quadratic fields are modular, Invent.
A $p$-Converse theorem for Real Quadratic Fields Le Hung, and Samir Siksek, Elliptic curves over real quadratic fields are modular, Invent
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.174274Z
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 0fc0a0bc-cf8e-46da-9df5-f6bb6ae90f9b · outbound
This paper cites Iwasawa theory for elliptic curves.
A $p$-Converse theorem for Real Quadratic Fields Iwasawa theory for elliptic curves
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-08-16T05:12:00.948412Z
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 7c819b85-15c9-474e-b2ce-9f58653d09b0 · outbound
This paper cites Gross and Don B.
A $p$-Converse theorem for Real Quadratic Fields Gross and Don B
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.164389Z
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 555e455b-d004-4bbd-aa61-aedf60be0af3 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.155640Z
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 8117a733-31e6-4ab1-8dbf-661cb44f5ed6 · outbound
This paper cites Press, Baltimore, MD, 1989, pp.
A $p$-Converse theorem for Real Quadratic Fields Press, Baltimore, MD, 1989, pp
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.145098Z
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 97313923-3135-46d4-8805-660903b6c50f · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.135590Z
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 bfa7abb2-229d-471e-a11f-a8b35fbdce7e · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.125242Z
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 d98dc3af-8c3c-45c3-97fc-2fc8f37f3d60 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T05:12:00.839716Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ef87de3b-27ed-4cd9-8817-53e90432dbec · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.108795Z
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 871947dd-67f2-4a6d-ab21-1abb94336c2f · outbound
This paper cites Iwasawa theory for quadratic Hilbert modular forms.
A $p$-Converse theorem for Real Quadratic Fields Iwasawa theory for quadratic Hilbert modular forms
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T05:12:00.847954Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6e0e3b91-1d5e-428e-8fe7-ece56a02f37a · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.097883Z
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 bfb2b2b1-4e50-45a1-a975-3e9d543c002a · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.086792Z
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 1afb1360-187a-4e00-bffb-2321aec85b64 · outbound
This paper cites 310, viii+559.
A $p$-Converse theorem for Real Quadratic Fields 310, viii+559
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.074813Z
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 7ac13c28-3b7a-4968-bd63-c51d57627f03 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.064701Z
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 3e206701-a09e-47c3-b341-319ff7008b9a · outbound
This paper cites Ryan, Gonzalo Tornar\'ia, and John Voight, Nonvanishing of twists of L -functions attached to H ilbert modular forms , LMS J.
A $p$-Converse theorem for Real Quadratic Fields Ryan, Gonzalo Tornar\'ia, and John Voight, Nonvanishing of twists of L -functions attached to H ilbert modular forms , LMS J
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.054319Z
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 c4feb68e-90f3-43d1-8b00-a54ea68943e1 · outbound
This paper cites Serre, Local class field theory, Algebraic N umber T heory ( P roc.
A $p$-Converse theorem for Real Quadratic Fields Serre, Local class field theory, Algebraic N umber T heory ( P roc
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:01.044412Z
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 0c14d098-b639-4496-b8e5-4edb74f423ae · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.034595Z
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 8ed158dd-2974-4854-acb7-0f4a8c3d603d · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T05:12:00.874427Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dc1400ea-34da-48d7-94db-a76c8d22dc54 · outbound
This paper cites Indivisibility of Heegner points in the multiplicative case.
A $p$-Converse theorem for Real Quadratic Fields Indivisibility of Heegner points in the multiplicative case
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T05:12:00.877548Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 41519df0-3c3d-47d1-998e-cb3a51b4d454 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.017154Z
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 beb91efc-d3d8-48de-b077-cdde2a47d102 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:01.006302Z
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 627d2c0f-e224-4a13-8291-dc3d17153eed · outbound
This paper cites Sigma 3 (2015), Paper No.
A $p$-Converse theorem for Real Quadratic Fields Sigma 3 (2015), Paper No
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:12:00.993687Z
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 7f0ab720-4455-4777-8b86-9177e81887ab · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:00.982568Z
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 71b63671-3c9e-41e2-b186-ad8a44a60475 · outbound
This paper cites an unresolved cited work.
A $p$-Converse theorem for Real Quadratic Fields Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:12:00.972529Z
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.