Paper Citation Record · LEDGER

The 3-adic valuations of Stirling numbers of the first kind

As of 8 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2109.13458.

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

pith.paper-citation-record.v1
2109.13458 v2

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T13:49:03.300019Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

33 of 33 outbound references displayed

verified exact0
verified fuzzy33
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2b4e1da4-78ee-4e57-a349-a34216a8f19e · outbound

This paper cites Adamchik, On Stirling numbers and Euler sums, J.

The 3-adic valuations of Stirling numbers of the first kind Adamchik, On Stirling numbers and Euler sums, J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.495508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 15251054-d445-4b19-b178-6ad04f9e9d58 · outbound

This paper cites Amdeberhan, D.

The 3-adic valuations of Stirling numbers of the first kind Amdeberhan, D

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.475349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8e8af123-4b3b-4127-abef-eea88f694949 · outbound

This paper cites Boyd, A p-adic study of the partial sums of the harmonic series, Experiment.

The 3-adic valuations of Stirling numbers of the first kind Boyd, A p-adic study of the partial sums of the harmonic series, Experiment

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.582241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a97dd022-bc9a-4393-81f2-33ed03cc22e9 · outbound

This paper cites Chen and M.

The 3-adic valuations of Stirling numbers of the first kind Chen and M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.481783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 39990ac3-f15b-4774-90c0-a447b57b65c0 · outbound

This paper cites Clarke, Hensel’s lemma and the divisibility by primes o f Stirling-like numbers, J.

The 3-adic valuations of Stirling numbers of the first kind Clarke, Hensel’s lemma and the divisibility by primes o f Stirling-like numbers, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.478744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 581e0269-e436-4e78-9159-2de08778b982 · outbound

This paper cites Comtet, Advanced combinatorics: The art of ﬁnite and inﬁnite expans ions, Revised and Enlarged Edition, D.

The 3-adic valuations of Stirling numbers of the first kind Comtet, Advanced combinatorics: The art of ﬁnite and inﬁnite expans ions, Revised and Enlarged Edition, D

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.553738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c67e1ca-5bf7-409e-a046-2b6fb06d69b6 · outbound

This paper cites Davis, Divisibility by 2 of Stirling-like numbers, Proc.

The 3-adic valuations of Stirling numbers of the first kind Davis, Divisibility by 2 of Stirling-like numbers, Proc

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.560209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cdab0e36-cfb1-45fa-b820-b2d3346b1ca5 · outbound

This paper cites Eswarathasan and E.

The 3-adic valuations of Stirling numbers of the first kind Eswarathasan and E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.548794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2554222e-c039-4e34-a757-9b05005e8fcf · outbound

This paper cites Erd˝ os and I.

The 3-adic valuations of Stirling numbers of the first kind Erd˝ os and I

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.567079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8cf0a9d9-8af9-4203-8614-1e83582d7cf7 · outbound

This paper cites Feng and M.

The 3-adic valuations of Stirling numbers of the first kind Feng and M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.542424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d34b31b8-3782-4b8f-b307-3f563b4f7aa5 · outbound

This paper cites Hong and M.

The 3-adic valuations of Stirling numbers of the first kind Hong and M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.563765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5b36f60c-5edc-4cf9-a8de-ae72f2660e0a · outbound

This paper cites Hong and C.L.

The 3-adic valuations of Stirling numbers of the first kind Hong and C.L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.538490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4a4d88c7-417a-46a0-b567-89d6113ffda3 · outbound

This paper cites Hong, J.R.

The 3-adic valuations of Stirling numbers of the first kind Hong, J.R

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.535172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ccc31cb2-c5e6-403f-8be0-bdf0b4248b3f · outbound

This paper cites Kamano, On 3-adic valuations of generalized harmonic numbers, Integers 12 (2012), 311-319.

The 3-adic valuations of Stirling numbers of the first kind Kamano, On 3-adic valuations of generalized harmonic numbers, Integers 12 (2012), 311-319

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.531751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e65e63ef-2e2a-4388-964b-2aea3c735792 · outbound

This paper cites Koblitz, p-Adic numbers, p-adic analysis and zeta-functions , 2nd ed., GTM 58, Springer-Verlag, New York.

The 3-adic valuations of Stirling numbers of the first kind Koblitz, p-Adic numbers, p-adic analysis and zeta-functions , 2nd ed., GTM 58, Springer-Verlag, New York

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.575834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31965d68-1e65-4017-a896-89b64e65ca47 · outbound

This paper cites Komatsu and P.

The 3-adic valuations of Stirling numbers of the first kind Komatsu and P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.525688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3f03a012-22aa-4b39-87d9-7e7b4c783c3d · outbound

This paper cites Lengyel, On the divisibility by 2 of Stirling numbers o f the second kind, Fibonacci Quart.

The 3-adic valuations of Stirling numbers of the first kind Lengyel, On the divisibility by 2 of Stirling numbers o f the second kind, Fibonacci Quart

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.522847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 95087b51-8f77-4c96-9d3b-44eb7a987426 · outbound

This paper cites Lengyel, On the 2-adic order of Stirling numbers of the second kind and their diﬀerences, DMTCS Proc.

The 3-adic valuations of Stirling numbers of the first kind Lengyel, On the 2-adic order of Stirling numbers of the second kind and their diﬀerences, DMTCS Proc

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.519426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3e7d7b1a-5bef-4b9d-917c-5cedf1ef6d61 · outbound

This paper cites Lengyel, Alternative proofs on the 2-adic order of Sti rling numbers of the second kind, Integers 10 (2010), 453-463.

The 3-adic valuations of Stirling numbers of the first kind Lengyel, Alternative proofs on the 2-adic order of Sti rling numbers of the second kind, Integers 10 (2010), 453-463

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.471643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ada36e36-5e65-4186-ad6a-1db85c606988 · outbound

This paper cites Lengyel, On p-adic properties of the Stirling numbers of the ﬁrst kind, J.

The 3-adic valuations of Stirling numbers of the first kind Lengyel, On p-adic properties of the Stirling numbers of the ﬁrst kind, J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.516037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0a29d409-c801-419f-87e3-043558d307f1 · outbound

This paper cites Leonetti and C.

The 3-adic valuations of Stirling numbers of the first kind Leonetti and C

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.512608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9fccda25-6593-44a4-9f94-ad3d1326c5a0 · outbound

This paper cites Lundell, A divisibility property for Stirling numb ers, J.

The 3-adic valuations of Stirling numbers of the first kind Lundell, A divisibility property for Stirling numb ers, J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.509520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e4295888-23e8-4f20-a94b-81af780ded17 · outbound

This paper cites Luo, S.F.

The 3-adic valuations of Stirling numbers of the first kind Luo, S.F

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.491875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d9cfa71a-1433-404b-a547-e91b15b24eb3 · outbound

This paper cites Miska, On p-adic valuations of Stirling numbers, Acta Arith.

The 3-adic valuations of Stirling numbers of the first kind Miska, On p-adic valuations of Stirling numbers, Acta Arith

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.557328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d84ba700-6b08-4a45-85b3-6665dc3602df · outbound

This paper cites Nagell, Eine Eigenschaft gewisser Summen, Skr.

The 3-adic valuations of Stirling numbers of the first kind Nagell, Eine Eigenschaft gewisser Summen, Skr

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.485235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 045cdaf7-4c5e-4238-819e-7b02c8e4658a · outbound

This paper cites Qiu and S.F.

The 3-adic valuations of Stirling numbers of the first kind Qiu and S.F

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.578781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b9f62216-f95a-4fd6-b85a-34562aa2caa3 · outbound

This paper cites Sanna, On the p-adic valuation of harmonic numbers, J.

The 3-adic valuations of Stirling numbers of the first kind Sanna, On the p-adic valuation of harmonic numbers, J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.488554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 26a6d939-431f-4dfe-91b7-edf2cbe55bc7 · outbound

This paper cites Theisinger, Bemerkung ¨ uber die harmonische Reihe, Monatsh.

The 3-adic valuations of Stirling numbers of the first kind Theisinger, Bemerkung ¨ uber die harmonische Reihe, Monatsh

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.546026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 11039e7f-4e26-4ad2-a913-5a89a8dc3b1a · outbound

This paper cites W ang and S.F.

The 3-adic valuations of Stirling numbers of the first kind W ang and S.F

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.528254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 49abbc1c-f8d9-4c49-b313-a70fa66cd86b · outbound

This paper cites W annermacker, On 2-adic orders of Stirling numbers of the second kind, Integers 5 (2005), A21.

The 3-adic valuations of Stirling numbers of the first kind W annermacker, On 2-adic orders of Stirling numbers of the second kind, Integers 5 (2005), A21

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.503480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0f421d70-4a2f-489f-88d9-d605307bf676 · outbound

This paper cites W u and Y.G.

The 3-adic valuations of Stirling numbers of the first kind W u and Y.G

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.498756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 350edfa8-22f1-4f02-8e4d-6e81b90d477d · outbound

This paper cites Zhao, S.F.

The 3-adic valuations of Stirling numbers of the first kind Zhao, S.F

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.570231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3f019cfa-0269-4d08-8bb5-1dcc7408377a · outbound

This paper cites Zhao, J.R.

The 3-adic valuations of Stirling numbers of the first kind Zhao, J.R

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:49:32.506457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.