Paper Citation Record · LEDGER

Counting matrices over finite rank multiplicative groups

As of 9 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2502.07100.

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

pith.paper-citation-record.v1
2502.07100 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T13:59:06.846746Z

measured 54 of 54 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

54 of 54 outbound references displayed

verified exact3
verified fuzzy35
unresolved16
parse uncertain0
malformed identifier0
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External citation measurements

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Outbound references

Observation a335f74c-1ca3-4c3b-bb5f-993fd98132fe · outbound

This paper cites Abrams, Z.

Counting matrices over finite rank multiplicative groups Abrams, Z

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.629601Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 88d632be-6932-4fca-908b-309c591bbbb9 · outbound

This paper cites Aﬁfurrahman, ‘Some counting questions for matrix products ’, Bull.

Counting matrices over finite rank multiplicative groups Aﬁfurrahman, ‘Some counting questions for matrix products ’, Bull

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.616820Z

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Observation ed10cfb3-d15c-4f5e-bdbf-0b99bf78d9a5 · outbound

This paper cites A uniform formula on the number of integer matrices with given determinant and height.

Counting matrices over finite rank multiplicative groups A uniform formula on the number of integer matrices with given determinant and height

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-08T13:59:06.656297Z

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Unavailable: canonical work link unavailable.

Observation 7a4e30aa-6ef7-428b-bf28-dc74a0f98861 · outbound

This paper cites Aﬁfurrahman, V.

Counting matrices over finite rank multiplicative groups Aﬁfurrahman, V

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.606029Z

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Observation a057efe2-cabf-48a8-8701-73cdaafbaf55 · outbound

This paper cites Ahmadi and I.

Counting matrices over finite rank multiplicative groups Ahmadi and I

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.595373Z

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Observation dd886f76-b126-45b0-9e91-7f4dd7fb54a9 · outbound

This paper cites Alon and J.

Counting matrices over finite rank multiplicative groups Alon and J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.584691Z

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Observation 95ec1e78-9700-401c-a730-16fb9d7b12c6 · outbound

This paper cites Amoroso, and E.

Counting matrices over finite rank multiplicative groups Amoroso, and E

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.574349Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 06a2f357-ba04-4b79-9e3a-ac2e31d8dcef · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.564215Z

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Observation 8c511d7f-ca08-4fe5-a50f-53a2ce42c1b3 · outbound

This paper cites Blomer and J.

Counting matrices over finite rank multiplicative groups Blomer and J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.553740Z

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Observation 3ad0037d-47ee-4c97-9397-f3cfe8a8dbd7 · outbound

This paper cites Blomer and C.

Counting matrices over finite rank multiplicative groups Blomer and C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.543857Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3acbbf73-bf71-4008-9acd-cdd56848a589 · outbound

This paper cites Bourgain, M.

Counting matrices over finite rank multiplicative groups Bourgain, M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.533873Z

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Observation 33284dbb-4752-492a-bf28-b8618e4e1bb2 · outbound

This paper cites Bourgain, V.

Counting matrices over finite rank multiplicative groups Bourgain, V

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.523498Z

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Observation 39387925-a69a-438f-94b3-e26ab0cb5ee2 · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.513181Z

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Observation 4875f5a7-21af-4b78-9304-e4aca1011448 · outbound

This paper cites Browning, W.

Counting matrices over finite rank multiplicative groups Browning, W

Reference 14

Resolution: verified exact; raw_fallback, observed 2026-08-08T13:59:07.127106Z

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Observation b0551603-7ecf-4176-91de-2ca20911f7ec · outbound

This paper cites Bulinski, A.

Counting matrices over finite rank multiplicative groups Bulinski, A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.503444Z

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Observation f6c761eb-7de5-4f01-a099-8bd2cf7d8a0b · outbound

This paper cites Bulinski and I.

Counting matrices over finite rank multiplicative groups Bulinski and I

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.493181Z

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Observation b94ff428-dcac-43b1-8d4e-ed49e7ec65b3 · outbound

This paper cites Campos, M.

Counting matrices over finite rank multiplicative groups Campos, M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.482553Z

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Observation 7eb94177-d63d-4a0e-8d8c-6993e2232698 · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.472231Z

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Observation 420c0e7b-1613-4ac1-9d97-0ca491192105 · outbound

This paper cites Eberhard, ‘The characteristic polynomial of a random matrix ’, Combina- torica, 42 (2022), 491–527.

Counting matrices over finite rank multiplicative groups Eberhard, ‘The characteristic polynomial of a random matrix ’, Combina- torica, 42 (2022), 491–527

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.461926Z

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Observation beaa1660-f8d1-4652-9d05-e34ed44d4aba · outbound

This paper cites Effective equidistribution of primitive rational points on expanding horospheres.

Counting matrices over finite rank multiplicative groups Effective equidistribution of primitive rational points on expanding horospheres

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-08T13:59:06.722774Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aee74765-9186-4253-bb38-f70cf48e2408 · outbound

This paper cites Eskin and Y.

Counting matrices over finite rank multiplicative groups Eskin and Y

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.451294Z

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Observation 35b0490e-834d-453e-a390-b214e49eebab · outbound

This paper cites Eskin, S.

Counting matrices over finite rank multiplicative groups Eskin, S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.441123Z

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Observation baeb8f99-4c0b-438d-9c2a-75ead013b1d0 · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.431317Z

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Observation 144cacb9-dce5-4612-a403-844e5190e3aa · outbound

This paper cites Feit and N.

Counting matrices over finite rank multiplicative groups Feit and N

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.421684Z

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Observation 41102f17-9455-47ec-9182-98fc07bf3743 · outbound

This paper cites Ferber, K.

Counting matrices over finite rank multiplicative groups Ferber, K

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.411415Z

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Observation 23f77fb8-9d26-44b6-95dd-d61ee5361247 · outbound

This paper cites Ferber, V.

Counting matrices over finite rank multiplicative groups Ferber, V

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.401234Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e2a007ef-8c78-4723-a70d-f04ca4296dd2 · outbound

This paper cites Fulman, ‘Random matrices theory over ﬁnite ﬁelds’, Bull.

Counting matrices over finite rank multiplicative groups Fulman, ‘Random matrices theory over ﬁnite ﬁelds’, Bull

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.389263Z

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Observation 14635930-056a-4900-a73a-609c5491a69d · outbound

This paper cites Fulman, and L.

Counting matrices over finite rank multiplicative groups Fulman, and L

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.378905Z

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Observation 9abcefa5-df79-4d31-93a4-3c6fdcce9ec1 · outbound

This paper cites Gerstenhaber, ‘On the number of nilpotent matrices with coe ﬃcients in a ﬁnite ﬁeld’, Illinois J.

Counting matrices over finite rank multiplicative groups Gerstenhaber, ‘On the number of nilpotent matrices with coe ﬃcients in a ﬁnite ﬁeld’, Illinois J

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.368551Z

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Observation aacb44c2-dcae-432f-bac9-6682c29955c8 · outbound

This paper cites Gorodnik, A.

Counting matrices over finite rank multiplicative groups Gorodnik, A

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.357974Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a86d868e-3e19-44aa-91d5-3da609a3164f · outbound

This paper cites Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices.

Counting matrices over finite rank multiplicative groups Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-08T13:59:06.762704Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d17f7a4-7d8e-48f5-9b0d-12caac649ff6 · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.347843Z

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Observation f72723b3-8e64-4b81-a8c4-7a8caaa7606e · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.337505Z

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Observation 0ed2a7ef-55d7-4710-b2ad-a9f2ed9439ef · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.327227Z

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Observation ed37a11e-0699-41c3-9081-c54fe5445c0e · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.316883Z

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Observation 37d2422a-6d33-4421-87d9-92586de78c5a · outbound

This paper cites Koplewitz, ‘The corank of a rectangular random integer matr ix’,Lin.

Counting matrices over finite rank multiplicative groups Koplewitz, ‘The corank of a rectangular random integer matr ix’,Lin

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.305665Z

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Observation 482d25c6-1568-4b5f-b59f-259939e95a42 · outbound

This paper cites Kwan and L.

Counting matrices over finite rank multiplicative groups Kwan and L

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.295275Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 280e46ca-829c-44ec-abdf-3500e02f77e9 · outbound

This paper cites Number of characteristic polynomials of matrices with bounded height.

Counting matrices over finite rank multiplicative groups Number of characteristic polynomials of matrices with bounded height

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-08T13:59:07.029864Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 21245764-939e-4b5b-ae0a-eb3be7058396 · outbound

This paper cites Mohammadi, A.

Counting matrices over finite rank multiplicative groups Mohammadi, A

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.284827Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e508233b-e71b-44dd-b287-7866de6a5769 · outbound

This paper cites On commuting pairs in arbitrary sets of 2x2 matrices.

Counting matrices over finite rank multiplicative groups On commuting pairs in arbitrary sets of 2x2 matrices

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-08T13:59:06.795258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9373d9e3-64ac-4ae3-886d-44a6b5b6eb6b · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.274970Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 11c9df4a-026d-4243-b566-4326a00c9bdd · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.264701Z

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Observation 238834ea-e0a9-4603-8103-c3c3338fd13c · outbound

This paper cites Ostafe and I.

Counting matrices over finite rank multiplicative groups Ostafe and I

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-08T13:59:06.806376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9505db65-02fb-467a-8129-2596d43410ba · outbound

This paper cites Reiner, ‘On the number of matrices with given characteristic p olynomial’, Illinois J.

Counting matrices over finite rank multiplicative groups Reiner, ‘On the number of matrices with given characteristic p olynomial’, Illinois J

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.253665Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6b846758-4451-4c5f-9234-11d5141f3203 · outbound

This paper cites Sanna, ‘On the distribution of the entries of a ﬁxed-rank ran dom matrix over a ﬁnite ﬁeld’, Finite Fields Appl.

Counting matrices over finite rank multiplicative groups Sanna, ‘On the distribution of the entries of a ﬁxed-rank ran dom matrix over a ﬁnite ﬁeld’, Finite Fields Appl

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.241653Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bb11e2ff-a0fa-4082-9115-b46084f7e4c9 · outbound

This paper cites Schmidt, ‘The subspace theorem in diophantine approximation s,” Compos.

Counting matrices over finite rank multiplicative groups Schmidt, ‘The subspace theorem in diophantine approximation s,” Compos

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.230310Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7d06be15-381d-46c4-8d2f-77e61e6e3262 · outbound

This paper cites Shah, ‘Counting integral matrices with a given characteristic polynomial’, Sankhya: The Indian J.

Counting matrices over finite rank multiplicative groups Shah, ‘Counting integral matrices with a given characteristic polynomial’, Sankhya: The Indian J

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.219074Z

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Observation 58dd9823-7f79-4321-8772-106bede5c26d · outbound

This paper cites Shapira and C.

Counting matrices over finite rank multiplicative groups Shapira and C

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.207850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c31adddf-6749-45a2-84d1-2c2a3e91d143 · outbound

This paper cites On the determinants of matrices with elements from arbitrary sets.

Counting matrices over finite rank multiplicative groups On the determinants of matrices with elements from arbitrary sets

Reference 49

Resolution: verified exact; local_arxiv, observed 2026-08-08T13:59:06.883475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ee479e20-6b94-4e17-b7f9-d1d1e89ad2b8 · outbound

This paper cites an unresolved cited work.

Counting matrices over finite rank multiplicative groups Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-08T13:59:07.195897Z

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Observation 7a222c58-e804-4346-92a8-656bb24d7ea3 · outbound

This paper cites Tao and V.

Counting matrices over finite rank multiplicative groups Tao and V

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.184250Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 933599b0-26d0-4b46-8c80-106547649eb6 · outbound

This paper cites Vu, ‘Recent progress in combinatorial random matrix theory ’, Probability Surveys, 18 (2021), 179–200.

Counting matrices over finite rank multiplicative groups Vu, ‘Recent progress in combinatorial random matrix theory ’, Probability Surveys, 18 (2021), 179–200

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.173294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1dd15604-f1cc-43a7-96b1-41d9763fbc10 · outbound

This paper cites Wei and F.

Counting matrices over finite rank multiplicative groups Wei and F

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.162245Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation db510976-3471-46ca-af17-d3fb5251db36 · outbound

This paper cites cn´2 “ 0, A´µpnq, c n´1 “ 0 and cn´2 ‰ 0, A´νpnq, c n´1 ‰ 0, where βpnq is given by ( B.1) and furthermore λpnq “ $ ’ ’ ’ ’ ’ & ’ ’ ’ ’ ’ % 1{2, n “ 5, 1, n.

Counting matrices over finite rank multiplicative groups cn´2 “ 0, A´µpnq, c n´1 “ 0 and cn´2 ‰ 0, A´νpnq, c n´1 ‰ 0, where βpnq is given by ( B.1) and furthermore λpnq “ $ ’ ’ ’ ’ ’ & ’ ’ ’ ’ ’ % 1{2, n “ 5, 1, n

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T13:59:07.150798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.