Paper Citation Record · LEDGER

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents

As of 19 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2502.05705.

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pith.paper-citation-record.v1
2502.05705 v1

Coverage vector

measured 39 of 39 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-08T18:25:48.917993Z

measured 39 of 39 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

39 of 39 outbound references displayed

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verified fuzzy28
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Outbound references

Observation ef096a83-510a-4567-ab9b-6f162a5223c5 · outbound

This paper cites Integers expressible as the sum of two rational cubes, 2024.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Integers expressible as the sum of two rational cubes, 2024

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.259098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation afcf8ec7-1e36-4dec-b5dc-c5fde169b80e · outbound

This paper cites Notes on elliptic curves (ii).

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Notes on elliptic curves (ii)

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.251018Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 61c58e43-0694-4a3a-b92d-a681ecead570 · outbound

This paper cites an unresolved cited work.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-08T18:25:49.242904Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c523dc0e-821c-48af-81fe-341314ab574a · outbound

This paper cites Counting cubic extensions with given quadratic resolvent.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Counting cubic extensions with given quadratic resolvent

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.234645Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9929cbf0-c7a5-4412-87ff-5d0bfb0e28ba · outbound

This paper cites Dirichlet series associated to quartic fields with given cubic resolvent.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Dirichlet series associated to quartic fields with given cubic resolvent

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.226347Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 164a0aa8-f40b-4be7-ab73-80ba70533f97 · outbound

This paper cites Rational Points on Modular Elliptic Curves.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Rational Points on Modular Elliptic Curves

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.217784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fdc054f1-0422-4bdc-a178-4addf643bed6 · outbound

This paper cites On the B irch- S winnerton- D yer quotients modulo squares.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On the B irch- S winnerton- D yer quotients modulo squares

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.209257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a7b8e98c-71b8-4fa3-b3f0-871a875ad21f · outbound

This paper cites Stark points and p -adic iterated integrals attached to modular forms of weight one.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Stark points and p -adic iterated integrals attached to modular forms of weight one

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.200238Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fa71adc6-2a52-46a5-a832-3eeb5799d1c2 · outbound

This paper cites Algebraic cycles and S tark- H eegner points.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Algebraic cycles and S tark- H eegner points

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.191393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a7fc378e-b3c3-421c-9b58-077015132c88 · outbound

This paper cites Conjectures on elliptic curves over quadratic fields.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Conjectures on elliptic curves over quadratic fields

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.182865Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5123617-ea98-495b-a9dd-02a909a4ad61 · outbound

This paper cites Kolyvagin’s work on modular elliptic curves in L -functions and arithmetic ( D urham, 1989).

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Kolyvagin’s work on modular elliptic curves in L -functions and arithmetic ( D urham, 1989)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.174363Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7f905e83-4a81-4adf-a6e1-9ecf830a467a · outbound

This paper cites Heegner points and derivatives of L -series.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Heegner points and derivatives of L -series

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.165661Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 65d5f167-0373-4e9b-8e1f-6a6dc0457a3f · outbound

This paper cites Heath-Brown.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Heath-Brown

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.842990Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef235de9-0b28-4fd6-8ec9-22b29193ec23 · outbound

This paper cites an unresolved cited work.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-08T18:25:49.151636Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 84a72b09-87ac-457e-ab03-5f94d7d12d21 · outbound

This paper cites On the ranks of the 2- S elmer groups of twists of a given elliptic curve.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On the ranks of the 2- S elmer groups of twists of a given elliptic curve

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.848604Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33871fb9-25b7-4f2f-b39e-01e0d865b7ea · outbound

This paper cites Rank growth of elliptic curves in S_4 and A_4 quartic extensions of the rationals, 2022.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Rank growth of elliptic curves in S_4 and A_4 quartic extensions of the rationals, 2022

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.137813Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b0fb77aa-9b85-4b10-a4b4-6c52694799de · outbound

This paper cites urgen Kl\.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents urgen Kl\

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.128989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 489142a6-1e79-4312-b0ed-a04d40056f85 · outbound

This paper cites Disparity in S elmer ranks of quadratic twists of elliptic curves.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Disparity in S elmer ranks of quadratic twists of elliptic curves

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.856874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d66ddf50-67fb-4b3f-b8d5-16c74c83c4ef · outbound

This paper cites A M arkov model for S elmer ranks in families of twists.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents A M arkov model for S elmer ranks in families of twists

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.115554Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3c6a55db-e484-4beb-9aeb-2701f20c8175 · outbound

This paper cites On M alle's conjecture for nilpotent groups.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On M alle's conjecture for nilpotent groups

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.106815Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 61e23cc1-b532-476c-95bd-3ed04e4a6792 · outbound

This paper cites Sums of rational cubes and the 3 -selmer group, 2024.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Sums of rational cubes and the 3 -selmer group, 2024

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.097814Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a702ba37-ca3a-4827-88db-369153a8ce16 · outbound

This paper cites Rank growth of elliptic curves in non-abelian extensions.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Rank growth of elliptic curves in non-abelian extensions

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.089060Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a7a12200-76d2-49e2-a516-067d215a8578 · outbound

This paper cites On the Distribution of Galois Groups.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On the Distribution of Galois Groups

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.080422Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 56d2d7a6-3022-4761-9f3b-18fdf7c8ea2e · outbound

This paper cites On the Distribution of Galois Groups, II.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On the Distribution of Galois Groups, II

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.072125Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cddf60c5-db5f-43c8-b41d-f80d1b90019e · outbound

This paper cites The S ato- T ate conjecture and generalizations.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents The S ato- T ate conjecture and generalizations

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.063468Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 78790ac5-6b08-4239-9932-6a5679b5be0a · outbound

This paper cites Finding large S elmer rank via an arithmetic theory of local constants.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Finding large S elmer rank via an arithmetic theory of local constants

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.879053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0dae59c-573e-4367-b967-fb2ec423b92e · outbound

This paper cites Mazur and K.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Mazur and K

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.049857Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b19b4607-3b03-43c7-b249-d78cc72d55b2 · outbound

This paper cites On the prime Selmer ranks of cyclic prime twist families of elliptic curves over global function fields.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents On the prime Selmer ranks of cyclic prime twist families of elliptic curves over global function fields

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-08T18:25:48.974666Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b27f4c16-12e4-41c0-bec9-8f59e6c13186 · outbound

This paper cites Arithmetic Statistics of Selmer Groups of Twist Families of Elliptic Curves Over Global Fields.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Arithmetic Statistics of Selmer Groups of Twist Families of Elliptic Curves Over Global Fields

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.041419Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5df89c0d-3e41-40a9-b651-05537378045c · outbound

This paper cites Random maximal isotropic subspaces and selmer groups.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Random maximal isotropic subspaces and selmer groups

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.032775Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation af2295dc-98b1-4021-8634-14e44eff0a64 · outbound

This paper cites Rank stability of elliptic curves in certain non-abelian extensions.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Rank stability of elliptic curves in certain non-abelian extensions

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-08T18:25:48.962681Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ab3c7b02-d9c2-4129-8f1b-53f1471ba13c · outbound

This paper cites The effect of twisting on the 2- S elmer group.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents The effect of twisting on the 2- S elmer group

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.897065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e755b62-209a-4867-b5e7-7824a5faa026 · outbound

This paper cites Silverman.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Silverman

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.018936Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 503b683c-ad79-4269-9b85-8eff50785bc3 · outbound

This paper cites The distribution of $\ell^\infty$-Selmer groups in degree $\ell$ twist families I.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents The distribution of $\ell^\infty$-Selmer groups in degree $\ell$ twist families I

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.902594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68bc30e9-5fcc-4083-b30b-e4212d373722 · outbound

This paper cites The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-08T18:25:48.905708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 786f6fa8-c10f-4822-b6a1-d41023d1ab8e · outbound

This paper cites Elliptic curves and analogies between number fields and function fields.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Elliptic curves and analogies between number fields and function fields

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.010290Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a86c0e9d-cfc1-4a83-bac1-3a407cb156e2 · outbound

This paper cites Heights of H eegner points on S himura curves.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Heights of H eegner points on S himura curves

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:49.001245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a92994d0-963c-42e7-81a0-bd8cbb107f0b · outbound

This paper cites Selmer groups and the indivisibility of H eegner points.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Selmer groups and the indivisibility of H eegner points

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:48.992479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1fdb51fb-0b1f-4833-b575-cf1b6f1f35b4 · outbound

This paper cites Gross-Zagier Formula for GL(2), II , page 191–242.

Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents Gross-Zagier Formula for GL(2), II , page 191–242

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:25:48.983535Z

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