Paper Citation Record · LEDGER

On the $p$-adic properties of Stirling numbers of the first kind

As of 16 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:1908.05594.

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

pith.paper-citation-record.v1
1908.05594 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:21:26.652909Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

36 of 36 outbound references displayed

verified exact0
verified fuzzy14
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e92efcfc-bb50-4e47-8465-029d0ea471fe · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Adamchik, On Stirling numbers and Euler sums, J

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.363474Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 937f723a-faae-453c-8e5e-52f260c9d91d · outbound

This paper cites Adelberg, The p-adic analysis of Stirling numbers via higher order Bernoul li numbers, Int.

On the $p$-adic properties of Stirling numbers of the first kind Adelberg, The p-adic analysis of Stirling numbers via higher order Bernoul li numbers, Int

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.593061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4d945152-8066-4258-ac92-06d6cf8c2e70 · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Boyd, A p-adic study of the partial sums of the harmonic series, Experiment

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.378246Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6589e168-0435-46a9-a3d4-7d7e1c5e8a5d · outbound

This paper cites Chen and M.

On the $p$-adic properties of Stirling numbers of the first kind Chen and M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.518750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8185550b-6ee9-4abc-bf4f-4e46c01ff5a6 · outbound

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

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

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.392894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7934792e-5eac-4178-a847-d58a95c2b928 · outbound

This paper cites Eswarathasan and E.

On the $p$-adic properties of Stirling numbers of the first kind Eswarathasan and E

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.404880Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6dd904ea-6444-4a48-bc8c-e724ba475b2e · outbound

This paper cites Erd˝ os and I.

On the $p$-adic properties of Stirling numbers of the first kind Erd˝ os and I

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.414096Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f549e21-c610-43e8-ab5d-4421df2f71e3 · outbound

This paper cites Feng, S.F.

On the $p$-adic properties of Stirling numbers of the first kind Feng, S.F

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.375804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7ad9965b-2bde-4dcc-abff-845dcab775cd · outbound

This paper cites Hong, Notes on Glaisher’s congruences, Chinese Ann.

On the $p$-adic properties of Stirling numbers of the first kind Hong, Notes on Glaisher’s congruences, Chinese Ann

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.344092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 11e0b418-efdf-40ee-bee5-826566dd910c · outbound

This paper cites Hong and C.L.

On the $p$-adic properties of Stirling numbers of the first kind Hong and C.L

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.309202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a8dcf212-ba83-4e74-8443-6cc1f76151f6 · outbound

This paper cites an unresolved cited work.

On the $p$-adic properties of Stirling numbers of the first kind Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:21:27.279420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eeed64e5-7142-4f62-b3f8-11d4f5b84bd0 · outbound

This paper cites Hsu and P.J-S.

On the $p$-adic properties of Stirling numbers of the first kind Hsu and P.J-S

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.250348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e599645c-962a-44c2-9c46-1439615980b4 · outbound

This paper cites Ireland and M.

On the $p$-adic properties of Stirling numbers of the first kind Ireland and M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:27.217597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation aa767954-e19f-49e2-93e3-27f3b122fb32 · outbound

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

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

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.466273Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05cf63b7-897e-4542-a4a0-b2b2619fdde0 · outbound

This paper cites Koblitz, p-Adic numbers, p-adic analysis and zeta-functions , 2nd ed., GTM 58, Springer-Verlag, New York, 1984.

On the $p$-adic properties 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, 1984

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.472642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 513b4340-2f3b-4118-9db9-6c6d1533eba7 · outbound

This paper cites Komatsu and P.

On the $p$-adic properties of Stirling numbers of the first kind Komatsu and P

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.480659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0c30394-a9b1-4d13-9612-49ed4e8d471a · outbound

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

On the $p$-adic properties 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: unresolved; no resolver link, observed 2026-08-14T13:21:26.487409Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df98430f-46c9-42c4-acbd-44d23a1caa0f · outbound

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

On the $p$-adic properties 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: unresolved; no resolver link, observed 2026-08-14T13:21:26.496496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32fc4b69-f91a-4422-a42e-543f83e06424 · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Lengyel, On p-adic properties of the Stirling numbers of the ﬁrst kind, J

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.503795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6edc3fef-847a-45d4-8f8e-03195d04a9a5 · outbound

This paper cites Leonetti and C.

On the $p$-adic properties of Stirling numbers of the first kind Leonetti and C

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.512097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5740774-7155-45c3-a2cf-eaa33d82a51e · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Lundell, A divisibility property for Stirling numb ers, J

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.522456Z

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Unavailable: canonical work link unavailable.

Observation ba0aa386-ce0a-4325-be9b-b7010e485106 · outbound

This paper cites Luo, S.F.

On the $p$-adic properties of Stirling numbers of the first kind Luo, S.F

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.529374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dac1c932-c488-4a84-bcb7-bd280e2042fc · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Miska, On p-adic valuations of Stirling numbers, Acta Arith

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.535998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddbdccca-958d-44ae-bc59-2b672b04b0d5 · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Nagell, Eine Eigenschaft gewisser Summen, Skr

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.542928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c01dc64e-ee9f-493a-bd47-28940a66f742 · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Theisinger, Bemerkung ¨ uber die harmonische Reihe, Monatsh

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.548352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6271bff-a0f6-4c90-8d95-acd40056c23d · outbound

This paper cites Qiu, Y.L.

On the $p$-adic properties of Stirling numbers of the first kind Qiu, Y.L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.964457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a7ae5bbf-dbce-4afd-bb0a-5d67da8d1398 · outbound

This paper cites Qiu and S.F.

On the $p$-adic properties of Stirling numbers of the first kind Qiu and S.F

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.561883Z

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Unavailable: canonical work link unavailable.

Observation 156d940f-3a2a-47ad-9a8a-a8d9bec4ff84 · outbound

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

On the $p$-adic properties of Stirling numbers of the first kind Sanna, On the p-adic valuation of harmonic numbers, J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.567719Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b72f9171-4519-4ba4-9bc2-72df45a1d0b3 · outbound

This paper cites S´ eroul, Programming for Mathematicians , Springer-Verlag, Berlin, 2000.

On the $p$-adic properties of Stirling numbers of the first kind S´ eroul, Programming for Mathematicians , Springer-Verlag, Berlin, 2000

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.909574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c00ba178-9c9f-4781-bb40-c58afa2bc868 · outbound

This paper cites W ang and S.F.

On the $p$-adic properties of Stirling numbers of the first kind W ang and S.F

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.879615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 38a8f7be-c940-4892-a590-58a4625d546e · outbound

This paper cites W ashington, Introduction to cyclotomic ﬁelds , Springer-Verlag New York Inc., 1982.

On the $p$-adic properties of Stirling numbers of the first kind W ashington, Introduction to cyclotomic ﬁelds , Springer-Verlag New York Inc., 1982

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.848503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2c078ef9-a536-4308-b8f4-cc2020ffd65b · outbound

This paper cites W ashington, p-Adic L-function and sums of powers, J.

On the $p$-adic properties of Stirling numbers of the first kind W ashington, p-Adic L-function and sums of powers, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.823929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7abf61be-52bb-4b69-beb1-d64aa46775de · outbound

This paper cites W olstenholme, On certain properties of prime numbers , Quart.

On the $p$-adic properties of Stirling numbers of the first kind W olstenholme, On certain properties of prime numbers , Quart

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.783878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e020c725-0074-4f0f-b00c-5c39632ac117 · outbound

This paper cites an unresolved cited work.

On the $p$-adic properties of Stirling numbers of the first kind Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:21:26.755373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bda4cf25-fb1a-4648-b33c-fe7fbb5420be · outbound

This paper cites Zhao, S.F.

On the $p$-adic properties of Stirling numbers of the first kind Zhao, S.F

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-14T13:21:26.643620Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 039b6eac-0fba-44a7-a2d3-f3289224d0fe · outbound

This paper cites Zhao, J.R.

On the $p$-adic properties of Stirling numbers of the first kind Zhao, J.R

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:21:26.716762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.