Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T10:34:23.664698Z
Paper Citation Record · LEDGER
Maximal order for divisor functions and zeros of the Riemann zeta-function
As of 13 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2411.19259.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
30 of 30 outbound references displayed
- verified exact0
- verified fuzzy22
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 497ca459-1492-4988-afad-84ce37494861 · outbound
This paper cites Akatsuka, The Euler product for the Riemann zeta-func tion in the critical strip, Kodai Math.
Maximal order for divisor functions and zeros of the Riemann zeta-function Akatsuka, The Euler product for the Riemann zeta-func tion in the critical strip, Kodai Math
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.124975Z
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 2e935bb5-899d-403e-b793-c562f5ba7eb8 · outbound
This paper cites Alaoglu and P.
Maximal order for divisor functions and zeros of the Riemann zeta-function Alaoglu and P
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.110462Z
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 6092ba0e-8f77-4a7a-a252-b2d4d6827730 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:24.096101Z
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 95f44c52-9ff6-48b0-aed7-c4dc709597d9 · outbound
This paper cites Broughan, Equivalents of the Riemann hypothesis.
Maximal order for divisor functions and zeros of the Riemann zeta-function Broughan, Equivalents of the Riemann hypothesis
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.082065Z
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 ad5a9379-2868-475a-bb6a-f792e69c918b · outbound
This paper cites Broughan, Equivalents of the Riemann hypothesis.
Maximal order for divisor functions and zeros of the Riemann zeta-function Broughan, Equivalents of the Riemann hypothesis
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.068020Z
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 82bff3f7-50eb-4637-9e5d-40575ce88fbc · outbound
This paper cites Caveney, J.-L.
Maximal order for divisor functions and zeros of the Riemann zeta-function Caveney, J.-L
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.054165Z
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 084f1ebf-b58a-4fbb-a39a-4e2b178ea487 · outbound
This paper cites Erd˝ os and J.-L.
Maximal order for divisor functions and zeros of the Riemann zeta-function Erd˝ os and J.-L
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.040080Z
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 c65e32fd-afb4-48da-9981-0574057189c1 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:24.026341Z
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 66cb4589-9d5e-4e30-8931-2f7a96b68c90 · outbound
This paper cites Lagarias, An elementary problem equivalent to the Rie mann hypothesis, Amer.
Maximal order for divisor functions and zeros of the Riemann zeta-function Lagarias, An elementary problem equivalent to the Rie mann hypothesis, Amer
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:24.012015Z
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 d72b774f-7241-43ea-a63a-b72d41e1ebf0 · outbound
This paper cites Lang, Introduction to transcendental numbers, Addi son–Wesley Publishing Co.
Maximal order for divisor functions and zeros of the Riemann zeta-function Lang, Introduction to transcendental numbers, Addi son–Wesley Publishing Co
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.997311Z
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 4cc2928e-b1b7-4308-97a5-ee9ff45ef320 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.983102Z
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 3f3c308a-7280-4b2f-8dd5-cb020725a83e · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.969433Z
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 b3bed4ce-0b68-475f-a895-04340f15b272 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.955805Z
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 f6fbf0e1-6a60-4ea8-b27f-41c7b4a08473 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.940886Z
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 8585d52f-95d9-49ae-919d-77a953c3d772 · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.926845Z
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 ae92cb38-9688-4fb9-8174-8e7d4eef5133 · outbound
This paper cites Nazardonyavi and S.
Maximal order for divisor functions and zeros of the Riemann zeta-function Nazardonyavi and S
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.912819Z
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 12aed41c-9855-4410-96c3-48d276871809 · outbound
This paper cites Ramanu jan revisited (Urbana-Champaign, Ill., 1987).
Maximal order for divisor functions and zeros of the Riemann zeta-function Ramanu jan revisited (Urbana-Champaign, Ill., 1987)
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.898386Z
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 1ca2d637-d1e0-4dff-a516-be78ba79676f · outbound
This paper cites Analytic number theory, mo dular forms and q-hypergeometric series.
Maximal order for divisor functions and zeros of the Riemann zeta-function Analytic number theory, mo dular forms and q-hypergeometric series
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.884297Z
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 8134596c-0ef1-47c4-a731-4c8cee6268f5 · outbound
This paper cites Nicolas and J.
Maximal order for divisor functions and zeros of the Riemann zeta-function Nicolas and J
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.870214Z
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 c87c0924-8b27-47f7-a0e7-3cae24c3f930 · outbound
This paper cites Ramanujan, Highly composite numbers, Proc.
Maximal order for divisor functions and zeros of the Riemann zeta-function Ramanujan, Highly composite numbers, Proc
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.855612Z
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 7fe0e3d2-f53b-4612-acea-59bc1414ff11 · outbound
This paper cites Ramanujan, The lost notebook and other unpublished p apers, with introduction by G.
Maximal order for divisor functions and zeros of the Riemann zeta-function Ramanujan, The lost notebook and other unpublished p apers, with introduction by G
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.841150Z
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 496b04b6-bb19-4a40-9749-94b6476ed203 · outbound
This paper cites Ramanujan, Collected papers of Srinivasa Ramanujan , AMS Chelsea Publishing, Providence, RI, 2000.
Maximal order for divisor functions and zeros of the Riemann zeta-function Ramanujan, Collected papers of Srinivasa Ramanujan , AMS Chelsea Publishing, Providence, RI, 2000
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.826499Z
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 8fa004bf-2a3d-40a1-87d8-f26f363a7843 · outbound
This paper cites Ramanujan, Highly composite numbers.
Maximal order for divisor functions and zeros of the Riemann zeta-function Ramanujan, Highly composite numbers
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.810890Z
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 f6123d03-ea83-4fba-b880-3086f38a8703 · outbound
This paper cites Seminar on number theory, Paris 1981–82 (Paris, 1981/1982).
Maximal order for divisor functions and zeros of the Riemann zeta-function Seminar on number theory, Paris 1981–82 (Paris, 1981/1982)
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.794864Z
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 812d3b62-e7ce-43d5-b060-66baa92200b9 · outbound
This paper cites Robin, Grandes valeurs de la fonction somme des divis eurs et hypoth` ese de Riemann, J.
Maximal order for divisor functions and zeros of the Riemann zeta-function Robin, Grandes valeurs de la fonction somme des divis eurs et hypoth` ese de Riemann, J
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.778245Z
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 63e89941-4fdc-44a5-b3ea-d5f75f46a95f · outbound
This paper cites Robin, Sur la diff´ erence Li( θ(x)) − π (x), Ann.
Maximal order for divisor functions and zeros of the Riemann zeta-function Robin, Sur la diff´ erence Li( θ(x)) − π (x), Ann
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.761897Z
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 adb1bfde-4de6-4d76-b82e-8908a54c6c2d · outbound
This paper cites an unresolved cited work.
Maximal order for divisor functions and zeros of the Riemann zeta-function Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T10:34:23.746928Z
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 48689e4d-0541-4432-98e4-d913f6d51f8a · outbound
This paper cites Tenenbaum, Introduction to analytic and probabilis tic number theory.
Maximal order for divisor functions and zeros of the Riemann zeta-function Tenenbaum, Introduction to analytic and probabilis tic number theory
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.731675Z
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 695e698f-ea6f-4db3-818c-a6423161275a · outbound
This paper cites The legacy of Srinivasa Ramanujan.
Maximal order for divisor functions and zeros of the Riemann zeta-function The legacy of Srinivasa Ramanujan
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.716577Z
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 0923828b-e85d-4413-84cd-199cb842b505 · outbound
This paper cites Wigert, Sur l’ordre de grandeur du nombre des diviseu rs d’un entier, Ark.
Maximal order for divisor functions and zeros of the Riemann zeta-function Wigert, Sur l’ordre de grandeur du nombre des diviseu rs d’un entier, Ark
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T10:34:23.700885Z
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
No inbound Pith citation observations are available.