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Paper Citation Record · LEDGER

Lower bounds for high moments of zeta sums

As of 12 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2506.09334.

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

pith.paper-citation-record.v1
2506.09334 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:56:24.589992Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

15 of 15 outbound references displayed

  • verified exact1
  • verified fuzzy8
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1eb1c851-9555-49e1-a7ba-f9df2a6cc0cb · outbound

This paper cites Zheng,High order moments of character sums, Proc.

Lower bounds for high moments of zeta sums Zheng,High order moments of character sums, Proc

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:26.516965Z

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.

source=pdf_text observed=2026-08-07T04:56:23.101361Z digest=sha256:d80bb3314c8ec8fd80e1dfa3e0ae4eb2102a9f0a2994bf7c1216fdaf1a3d7689

Observation fba6de9f-358a-43a5-87b5-e7e227f7dde9 · outbound

This paper cites Correlations of the Riemann zeta function.

Lower bounds for high moments of zeta sums Correlations of the Riemann zeta function

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:56:24.903714Z

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.

source=pdf_text observed=2026-08-07T04:56:23.230869Z digest=sha256:431b9a475f59aaaa6d16d1f1924075cc0b5af0cdc12313399805bb0af471c0a1

Observation 7434f7a8-6334-436a-9f9a-3e28ecfd31e4 · outbound

This paper cites de la Bret` eche, M.

Lower bounds for high moments of zeta sums de la Bret` eche, M

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:26.331623Z

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.

source=pdf_text observed=2026-08-07T04:56:23.283210Z digest=sha256:bcfae3086fd22f1a93ba3b616f4c6b8e339fe43e674f20b8b8aa5036b6c69e2c

Observation cde25c57-5554-420a-adb6-2baaa3012dac · outbound

This paper cites an unresolved cited work.

Lower bounds for high moments of zeta sums Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:56:26.207449Z

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.

source=pdf_text observed=2026-08-07T04:56:23.406723Z digest=sha256:43429304517b43d8e5033808e9663424331117783dd0ff9afa65fbb79e0a1f36

Observation da01da32-c358-4fb6-a2b5-824e6b9edbc7 · outbound

This paper cites Gao,Upper bounds for moments of zeta sums, J.

Lower bounds for high moments of zeta sums Gao,Upper bounds for moments of zeta sums, J

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:26.067944Z

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.

source=pdf_text observed=2026-08-07T04:56:23.512979Z digest=sha256:d4c6c517ca32cb491592fddbb4f821c6b075197dfb56e513362c74c14f56f8cb

Observation d0a7a52d-edc5-4362-b74b-b7c509b0cadd · outbound

This paper cites Granville and K.

Lower bounds for high moments of zeta sums Granville and K

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:25.939859Z

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.

source=pdf_text observed=2026-08-07T04:56:23.649739Z digest=sha256:4a1ba21657afea926cb3e3692898d67f2a6b0c9952f091393f98379f5b4cd329

Observation fec9dead-425e-415b-931b-7a073fb9cb0d · outbound

This paper cites an unresolved cited work.

Lower bounds for high moments of zeta sums Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:56:25.836790Z

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.

source=pdf_text observed=2026-08-07T04:56:23.722001Z digest=sha256:c14f3a2a28b4f933e7e3ac8512d93b7f079fb4d86427f502fff15a134b78aa38

Observation fd4ce65b-5e99-47b5-a65f-cb801c807b18 · outbound

This paper cites an unresolved cited work.

Lower bounds for high moments of zeta sums Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:56:25.697693Z

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.

source=pdf_text observed=2026-08-07T04:56:23.852139Z digest=sha256:97f6388fa04a58f3da7e46e2d16bf6c7c80c49382d6ade7f7a5cc06a9d8ef9d7

Observation d58505d9-a899-491d-ab39-e9bd61e39bd7 · outbound

This paper cites The typical size of character and zeta sums is $o(\sqrt{x})$.

Lower bounds for high moments of zeta sums The typical size of character and zeta sums is $o(\sqrt{x})$

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-07T04:56:23.985574Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:56:23.985574Z digest=sha256:f5cbd6286a37abf597daa2f6584926b7e4f063cc1e543a0f52a903ffd14ade1e

Observation 7acebae7-e025-4be6-a87e-0aeb04bf59c3 · outbound

This paper cites an unresolved cited work.

Lower bounds for high moments of zeta sums Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:56:25.570905Z

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.

source=pdf_text observed=2026-08-07T04:56:24.052880Z digest=sha256:a67c3a68ea9862ee28b2223a58c94f93f6a18f456656cf69d9a7201b4d8ce67b

Observation 1cfe45d0-6bfd-4f5c-907a-6c0f25af4c63 · outbound

This paper cites Munsch,Shifted moments of L-functions and moments of theta functions, Mathematika63 (2017), no.

Lower bounds for high moments of zeta sums Munsch,Shifted moments of L-functions and moments of theta functions, Mathematika63 (2017), no

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:25.443234Z

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.

source=pdf_text observed=2026-08-07T04:56:24.235791Z digest=sha256:6f90a9f0ccc762507b1c43e312b8b9a69a4b44a992dbf1030cec78495bf80791

Observation 7b9dee48-6472-4d02-a698-d9ef5c90a98a · outbound

This paper cites Munsch and I.

Lower bounds for high moments of zeta sums Munsch and I

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:25.304503Z

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.

source=pdf_text observed=2026-08-07T04:56:24.320954Z digest=sha256:0012c1a78ab01439f00377bc4aeb8c58711c78c8b1dce4ec3c078831a40b6127

Observation 9bd46f2d-ed5b-46c4-a91b-01f6b862b6ce · outbound

This paper cites Szab´ o,High moments of theta functions and character sums, Mathematika, pp.

Lower bounds for high moments of zeta sums Szab´ o,High moments of theta functions and character sums, Mathematika, pp

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:25.188246Z

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.

source=pdf_text observed=2026-08-07T04:56:24.423571Z digest=sha256:9a6c2799e21a7956ec3ebb80bc32d24510d8ce8010efb6d5e06f16399e73dbf9

Observation daf79efd-7ab4-44e2-a7e9-86c93e686868 · outbound

This paper cites A lower bound on high moments of character sums.

Lower bounds for high moments of zeta sums A lower bound on high moments of character sums

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-07T04:56:24.535361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:56:24.535361Z digest=sha256:ff30b43bec6ad2a147b135424b32025af055423f4f5478722972c4d8e732799e

Observation b0e57a89-8594-47fd-a2c1-ed83f040ada9 · outbound

This paper cites Yang,Extreme values of derivatives of zeta and L-functions, Bull.

Lower bounds for high moments of zeta sums Yang,Extreme values of derivatives of zeta and L-functions, Bull

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:56:25.072904Z

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.

source=pdf_text observed=2026-08-07T04:56:24.589992Z digest=sha256:ad04e40683237acf792ba2b83dc6eb12db64ba24133383363de3dcc7ddee896a

Pith citing papers

No inbound Pith citation observations are available.