Paper Citation Record · LEDGER

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis

As of 11 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2607.09797.

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

pith.paper-citation-record.v1
2607.09797 v3

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T08:06:03.886944Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

20 of 20 outbound references displayed

verified exact0
verified fuzzy0
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0721a355-80e9-4235-b627-8d18842f359d · outbound

This paper cites Riesz-type criteria for the Riemann hypothesis.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Riesz-type criteria for the Riemann hypothesis

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:02.663203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1318351-54dd-4bc7-ba81-8452b5a6368a · outbound

This paper cites Ayoub,An Introduction to the Analytic Theory of Numbers, American Mathematical Society, Providence, 1963.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Ayoub,An Introduction to the Analytic Theory of Numbers, American Mathematical Society, Providence, 1963

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:02.772829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a28546d-242d-4d5f-a0f6-33f129a88429 · outbound

This paper cites B´ aez-Duarte,M¨ obius convolutions and the Riemann hypothesis, Int.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis B´ aez-Duarte,M¨ obius convolutions and the Riemann hypothesis, Int

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:02.882787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa2cbaa0-a89f-4cb0-870f-42269e250d12 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:02.934329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bbb1c2a-7314-45ce-bd31-0bd046c72b69 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:02.992805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8426858b-efcd-4468-9937-9b4f99ac64e6 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.010530Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16aefd02-2b99-472e-a5e8-9fad3a7bb875 · outbound

This paper cites Davenport,Multiplicative Number Theory, 3rd ed., Graduate Texts in Mathematics 74, Springer-Verlag, New York, 2000.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Davenport,Multiplicative Number Theory, 3rd ed., Graduate Texts in Mathematics 74, Springer-Verlag, New York, 2000

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.070368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dab2a85e-45d7-43d7-8dbd-e95a43d58434 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.134556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 138a92fa-6783-4a36-9eb2-cc2efc73f8aa · outbound

This paper cites Garg and B.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Garg and B

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.192856Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b051f961-4d92-463e-a8c2-4e7b9efc88ef · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.258086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c08e5ac0-f8c3-4ec5-9bd0-ed7985c32109 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.315192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c7bfab0-af7d-463a-ba37-01c7ec6d0a94 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.376942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 310198c7-b769-4b8d-9ed5-71fc0dca957d · outbound

This paper cites Some explicit formulas for partial sums of M\"obius functions.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Some explicit formulas for partial sums of M\"obius functions

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.418889Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51951394-3c01-4d12-aec1-48417c503af7 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.485428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10689074-145a-4132-9d37-7bd8a34fa7d9 · outbound

This paper cites The Riemann hypothesis is true up to $3\cdot 10^{12}$.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis The Riemann hypothesis is true up to $3\cdot 10^{12}$

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.555565Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25cdcd46-a4a5-45af-ae1a-3930ebeea98e · outbound

This paper cites Riesz,Sur l’hypoth` ese de Riemann, Acta Math.40(1916), 185–190.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Riesz,Sur l’hypoth` ese de Riemann, Acta Math.40(1916), 185–190

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.629483Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaeee85a-00f4-4789-80f6-fbf461b1325e · outbound

This paper cites Rudin,Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Rudin,Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.686620Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b287319e-56cf-4974-b2de-2441d41591b3 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.761845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebd553b2-249c-46d8-8906-06fb92132aae · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.820812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 131c9957-2294-4a09-b5d9-96e39712bfd9 · outbound

This paper cites an unresolved cited work.

Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T08:06:03.886944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.