Paper Citation Record · LEDGER

The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

As of 23 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 11 inbound Pith citation observations for arXiv:2503.17619.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2503.17619 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 11 of 11 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:23:01.681321Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T15:37:06.647164Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation b59d0763-9202-4558-8537-dea26a8642e3 · inbound

Quadratic spaces and Selmer groups of abelian varieties with multiplication cites this paper.

Quadratic spaces and Selmer groups of abelian varieties with multiplication The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-16T05:23:01.681321Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e944a413-b8ca-4dd8-b9c8-1b0877aa928d · inbound

Elliptic curves of rank one over number fields cites this paper.

Elliptic curves of rank one over number fields The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T14:58:08.559546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b29240c-651e-46f9-8cf9-234a92612b09 · inbound

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two cites this paper.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.182734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a662b13d-3a48-422c-8059-a2078338d3cc · inbound

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants cites this paper.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T18:32:22.947839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d746d18f-bc0b-41e6-b11a-dcf7869048d2 · inbound

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography cites this paper.

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-03T08:37:23.401247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5e67b4d-5ac1-4899-8e08-38f119f06050 · inbound

A proof of $p$-adic Gross--Zagier theorem via BDP formula cites this paper.

A proof of $p$-adic Gross--Zagier theorem via BDP formula The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T11:46:17.800886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fbcaa45b-3a18-40eb-8564-bd49bb8cb1fe · inbound

A proof of $p$-adic Gross--Zagier theorem via BDP formula cites this paper.

A proof of $p$-adic Gross--Zagier theorem via BDP formula The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 1998

Resolution: unresolved; no resolver link, observed 2026-08-02T16:24:07.529941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a70e18de-d6b8-4eaa-9a5a-3612d289a900 · inbound

On the coefficients of the Taylor expansion of $L$-functions of elliptic curves cites this paper.

On the coefficients of the Taylor expansion of $L$-functions of elliptic curves The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:26:29.526390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bcf3e586-15af-4c2c-916a-119f28379985 · inbound

Recent Progress around Cohen-Lenstra Heuristics cites this paper.

Recent Progress around Cohen-Lenstra Heuristics The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 14

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T15:37:06.648710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e5dfae57-920c-430c-9262-792af3c7f9fe · inbound

Tamagawa ratios and unbounded Selmer moments cites this paper.

Tamagawa ratios and unbounded Selmer moments The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 55

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:45:47.017019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f3711460-04ea-4f0b-8f12-170ce133a429 · inbound

Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$ cites this paper.

Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$ The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-07T10:44:10.661681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.