Paper Citation Record · LEDGER

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation

As of 13 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 1 inbound Pith citation observation for arXiv:2504.09411.

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

pith.paper-citation-record.v1
2504.09411 v2

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-22T21:10:05.637821Z

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One-hop event checks from named stored sources.

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Pith citing papers itemized under the disclosed page cap.

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

Source: pith, observed 2026-08-07T15:07:27.344697Z

Reference resolution

52 of 52 outbound references displayed

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External citation measurements

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Outbound references

Observation e0a47620-0457-4ff5-95c2-aa3ed66a4510 · outbound

This paper cites Allen and V.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Allen and V

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.045335Z

Source-reported events for the cited work

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Observation 851b0b70-272b-4ee6-ad23-8ad69c1a4212 · outbound

This paper cites Badziahin and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Badziahin and S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.060108Z

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 8b69a882-9710-4e29-b55f-d63bb29836e2 · outbound

This paper cites Beresnevich, A.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich, A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.039628Z

Source-reported events for the cited work

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Observation c8244dbb-3a07-4d41-8e3f-65855bb0fa65 · outbound

This paper cites Beresnevich and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich and S

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.066397Z

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Observation 7ca6382b-5e30-4735-b96a-dbd29f1c189f · outbound

This paper cites Beresnevich and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich and S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.053860Z

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Observation 6992dcca-44d5-489d-9bde-cc84b17b7334 · outbound

This paper cites Beresnevich and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich and S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.042343Z

Source-reported events for the cited work

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Observation bdbd2727-0484-445d-b092-7824d0d956a8 · outbound

This paper cites Beresnevich and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich and S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.056982Z

Source-reported events for the cited work

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Observation 8c070d6f-c8c9-42f0-bb29-a565c48a2086 · outbound

This paper cites Beresnevich, A.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Beresnevich, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.048293Z

Source-reported events for the cited work

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Observation ff95dbd5-35de-4b41-8c41-360bc3a4f35f · outbound

This paper cites Bishop and Y.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Bishop and Y

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.036512Z

Source-reported events for the cited work

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Observation bb5c9d24-5d27-459c-869a-2a562181321a · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.051171Z

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Observation 23544b59-2eef-4e5f-8eaf-fb2a6148a5dc · outbound

This paper cites On the Exact Fourier Dimension of Sets of Well-Approximable Matrices.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation On the Exact Fourier Dimension of Sets of Well-Approximable Matrices

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-22T21:12:08.447565Z

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 39214212-2679-4ac1-bf2c-fc10369eebbd · outbound

This paper cites Chen and A.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Chen and A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.069813Z

Source-reported events for the cited work

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This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.073192Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c3170909-ff5d-4a4a-a183-79e862408be4 · outbound

This paper cites Chow and N.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Chow and N

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.154750Z

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 9e2aeed4-59b2-454d-8df6-b2f1bcf23f78 · outbound

This paper cites Chow and N.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Chow and N

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.135101Z

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 133edeae-f9b7-4fc2-94e0-0f5d838672a7 · outbound

This paper cites Chow and L.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Chow and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.177160Z

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 9540c747-cb72-4850-a141-3be812090b9a · outbound

This paper cites Ekstr¨ om.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Ekstr¨ om

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.109461Z

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 11198b21-8e19-4374-abec-113cf54db979 · outbound

This paper cites Ekstr¨ om, T.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Ekstr¨ om, T

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.112960Z

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 1b6e8d9e-afd2-4f63-904a-d88ed3681c94 · outbound

This paper cites Einsiedler, A.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Einsiedler, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.138787Z

Source-reported events for the cited work

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Observation 8b2fe764-bf66-483a-adad-d502b08af5cc · outbound

This paper cites Fourier decay of product measures.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Fourier decay of product measures

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-22T21:12:08.457475Z

Source-reported events for the cited work

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Observation ffcede8b-95f8-40cd-b0e3-42c47c7c62a9 · outbound

This paper cites Fraser and K.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Fraser and K

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.171489Z

Source-reported events for the cited work

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Observation 309cc3a6-bf8c-4140-bdd0-94ee15987e09 · outbound

This paper cites Gallagher.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Gallagher

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.179639Z

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 37f24d94-6df0-46ff-ae2b-1f8cef0ee8cd · outbound

This paper cites Gallagher.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Gallagher

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.157960Z

Source-reported events for the cited work

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Observation fbbf69b1-c1ae-4054-bd97-f437aec92364 · outbound

This paper cites Hambrook.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Hambrook

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.096981Z

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 24f77898-60b4-418f-bd9a-7e51122fcd96 · outbound

This paper cites Hambrook and H.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Hambrook and H

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.082679Z

Source-reported events for the cited work

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Observation 70b50ac9-7078-42d8-8568-b2e3607222f4 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.103061Z

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 de0f0eb1-d0ae-4366-8615-c1cd3b5bf4ae · outbound

This paper cites Hussain and D.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Hussain and D

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.142268Z

Source-reported events for the cited work

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Observation 04b3548a-50cf-4934-ad55-a079da0e289d · outbound

This paper cites Hussain and T.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Hussain and T

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.121982Z

Source-reported events for the cited work

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Observation 84e4b6ca-828c-413a-9db9-decbf6da616f · outbound

This paper cites Jarn ´ ık.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Jarn ´ ık

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.091489Z

Source-reported events for the cited work

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Observation dab93008-0958-4508-aee8-72dba28febe0 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.161383Z

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 e1d747f5-45ac-4df4-bf72-238385f58910 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.088800Z

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 69ca8a5d-4881-4390-96d2-71bb545ddf85 · outbound

This paper cites Koivusalo and M.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Koivusalo and M

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.131685Z

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 07dc74c8-b2f6-451a-8d04-4de91aad3c13 · outbound

This paper cites Khintchine.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Khintchine

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.085723Z

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 9f8c92aa-dc60-4a1d-92df-764aa0511f5a · outbound

This paper cites /suppress Laba and M.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation /suppress Laba and M

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.145489Z

Source-reported events for the cited work

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Observation efe4759e-835f-495c-af18-6f16944f3757 · outbound

This paper cites Lamperti.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Lamperti

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.164702Z

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 61ab7766-7f46-4368-855d-66324562c6fe · outbound

This paper cites Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-22T21:12:08.462391Z

Source-reported events for the cited work

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Observation 7b5bc5df-807b-406e-b3d8-b4220556a891 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.076336Z

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 ecdf036e-7cbc-48cf-a1f5-eeb74f41e7e9 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.079503Z

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 f604e409-0b04-4706-8b8a-9b9c97b1140f · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.106477Z

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 cfa56079-083a-4326-881b-1488e5ba8659 · outbound

This paper cites Pollington and S.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Pollington and S

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.093962Z

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 53f86129-82ed-4adc-8301-08e87446e3f6 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.116066Z

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 75ba1a27-bbca-4236-b5d8-e290376ea5e7 · outbound

This paper cites Rynne and H.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Rynne and H

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.168022Z

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 0c1c7ed6-7587-4105-bcdc-4b495216be89 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.033587Z

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 ad23294d-a7c9-4d13-b24f-aa83d048e5cb · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.063194Z

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 07546085-b1e8-4b04-845c-5cfe82fc3d3c · outbound

This paper cites Non-Salem sets in multiplicative Diophantine approximation.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Non-Salem sets in multiplicative Diophantine approximation

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-22T21:12:08.452561Z

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 c21ea091-9c46-4631-b3ba-d10aa7377933 · outbound

This paper cites Shieh and Y.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Shieh and Y

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.099918Z

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 16bd4497-d2d4-4b60-a597-6521a45eb2ca · outbound

This paper cites Sprindˇ zuk.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Sprindˇ zuk

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.119003Z

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 58fc65f9-fd81-4d08-b178-98082c6ea038 · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.174572Z

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 abbf0564-c031-4703-9b72-eee17938824b · outbound

This paper cites Wang and J.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Wang and J

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.128216Z

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 719dda84-c668-42dd-beac-2b9880a37afe · outbound

This paper cites Wang and J.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Wang and J

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.124997Z

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 a7eea4ee-244b-4bab-a53f-c742a9b37f37 · outbound

This paper cites A note on matrix approximation in the theory of multiplica tive Diophantine approx- imation.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation A note on matrix approximation in the theory of multiplica tive Diophantine approx- imation

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T21:12:09.148688Z

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 a82eef22-71a3-4255-83f5-181c2087cfcc · outbound

This paper cites an unresolved cited work.

Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-05-22T21:12:09.151524Z

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

Observation 80fdc144-ed66-48b2-a1e5-f4ff63b75bb3 · inbound

Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights cites this paper.

Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-07T15:07:27.470872Z

Source-reported events for the cited work

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