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Paper Citation Record · LEDGER

Bounds for moments of twisted quadratic characters of prime modulus

As of 20 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2608.05961.

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

pith.paper-citation-record.v1
2608.05961 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T20:21:54.958029Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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

29 of 29 outbound references displayed

  • verified exact3
  • verified fuzzy11
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3904d798-12ff-4860-af2f-3a02a385c2e4 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.644070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.816122Z digest=sha256:15318b7dee63bb71ae2b435807e8517406de1cc5775bb97d91de1e65186c5916

Observation 3d3eb35d-8dab-4bab-b5cb-a6e3e1b76c63 · outbound

This paper cites Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field.

Bounds for moments of twisted quadratic characters of prime modulus Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-07T20:21:55.166478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.821928Z digest=sha256:d11a4a697f8f4cac20bcbe230e4925630cec09803c607b83c4d82466d0cbee68

Observation 10c70102-fec7-4053-b411-7ec69478b9d0 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.628505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.827563Z digest=sha256:0734b3cef83106ddcd97baf8fefbc03e72b8949ca36b497cf2247ce67bd45f6d

Observation 1292d27a-8a9d-470a-84bc-72919a542adc · outbound

This paper cites Dirichlet $L$-functions of quadratic characters of prime conductor at the central point.

Bounds for moments of twisted quadratic characters of prime modulus Dirichlet $L$-functions of quadratic characters of prime conductor at the central point

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-07T20:21:55.143267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.832871Z digest=sha256:817f989d8eb5b2cd9ab0859ce47ce20dbc771300799d70296bdbb9dd402b343a

Observation 7b29d4eb-7a9e-45ef-8515-239d46197b6f · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.611992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.838606Z digest=sha256:61849fd3198fdf357aab5d9715eaf9bd1310489ad7c280088e33861efc4d6b30

Observation 8b1cde1d-832c-4f01-8161-7fb16e67463b · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.595829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.843734Z digest=sha256:0033565b0c9030c483a80b70155c1374a7eeeec058e88f650bfb896c91723b12

Observation b2c955c1-eb1e-47f9-871e-188bdd5b5e37 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.579364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.848887Z digest=sha256:72bddac5c4db68ac1809c016a0dab522fdba013e59d252be3f6bac5d5d2d82fb

Observation 2d151684-e17e-4d9c-9a4f-273159d9123c · outbound

This paper cites Gao and L.

Bounds for moments of twisted quadratic characters of prime modulus Gao and L

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.473966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.853714Z digest=sha256:980e8a1a093d3c0e6a80966f2e255e01f97ac274ad02502b743fe9d06ecdfd61

Observation b9b05673-3711-4c29-98fd-5334565413d7 · outbound

This paper cites Gao and L.

Bounds for moments of twisted quadratic characters of prime modulus Gao and L

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.456496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.858989Z digest=sha256:9d89140ca68ab2dbbc87f92ed2f585fdb7d0b8fc970ea3c2945c1c2f2ffecf8b

Observation 3e8452bd-ac14-41b6-af97-4c70a215d41f · outbound

This paper cites Gao and L.

Bounds for moments of twisted quadratic characters of prime modulus Gao and L

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.438414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.863649Z digest=sha256:40c8a5ddf11c4ba2ea11e31f08ed5dfe9b0de904d3fe8224b6d6eea82dfa9d99

Observation 7637a266-055b-4d93-923f-b37514481e33 · outbound

This paper cites Gao and L.

Bounds for moments of twisted quadratic characters of prime modulus Gao and L

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.420808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.868519Z digest=sha256:587f56335ed7779472a46e92714f41ced77c06dd9c6bb0d931167d198f4ff975

Observation 5372e55c-c7aa-4d5f-b588-a61103e1cd20 · outbound

This paper cites Bounds for Moments of Twisted Fourier coefficients of Modular Forms.

Bounds for moments of twisted quadratic characters of prime modulus Bounds for Moments of Twisted Fourier coefficients of Modular Forms

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-07T20:21:54.873353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T20:21:54.873353Z digest=sha256:df0a10cdc32ed4610f122cf455f9cb3cbda51ecbd0430e158da0444f8f0e1a8e

Observation 7fe4ea8b-99e4-4413-b97c-2f5bbe28799d · outbound

This paper cites Gao and Y.

Bounds for moments of twisted quadratic characters of prime modulus Gao and Y

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.404145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.878877Z digest=sha256:48ed63eff24c0fe4fd683e248371dc716630830c829d41b82992f0ea938a608e

Observation 05d88315-3c96-4e40-87a4-f2cd45dfdde2 · outbound

This paper cites Gao and Y.

Bounds for moments of twisted quadratic characters of prime modulus Gao and Y

Reference 14

Resolution
verified exact
raw_fallback, observed 2026-08-07T20:21:55.103203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.883808Z digest=sha256:578dd448868fd87cbc2e4e6816821916a8cdd3d588acdcb382cbd2aa8175e646

Observation 9899f295-aa68-4301-bddd-6efd72e25360 · outbound

This paper cites Goldfeld and X.

Bounds for moments of twisted quadratic characters of prime modulus Goldfeld and X

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.388049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.888792Z digest=sha256:9f9f2fe59227fcb3b26a84ee2c548505e361db5a53e8ec807bf961d8ef49a827

Observation 65d79443-382b-4591-9f05-fd354b926a93 · outbound

This paper cites Goldfeld and C.

Bounds for moments of twisted quadratic characters of prime modulus Goldfeld and C

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.371132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.893653Z digest=sha256:bef2f2c977fbba884f97c2e9e614298294df943cb549d976a332d1a2bd495569

Observation 807499fd-03f3-4ded-88dc-88fe3a709f1e · outbound

This paper cites Sharp conditional bounds for moments of the Riemann zeta function.

Bounds for moments of twisted quadratic characters of prime modulus Sharp conditional bounds for moments of the Riemann zeta function

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-07T20:21:54.898473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T20:21:54.898473Z digest=sha256:a0859d706926eec59beabb2346303219bc96c80028bdf3a687a82a212c06a1f7

Observation 58671933-f0ca-44bd-9f86-24be6d95a1de · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-07T20:21:54.903873Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T20:21:54.903873Z digest=sha256:a7a41ab392dff1acd6bec5a064019bda1c2509b263701668907478895a779ee7

Observation 8a7ff98e-3482-4579-a649-83bd38a04571 · outbound

This paper cites Iwaniec and E.

Bounds for moments of twisted quadratic characters of prime modulus Iwaniec and E

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.342009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.908775Z digest=sha256:0a9eb0b642d7dd607feefbe9b5629a34a7f48a31615f51ba1b4d05f619d34acb

Observation f6a0b8f7-653e-4184-9054-f09701c37264 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.325995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.913639Z digest=sha256:89050719382170fdbab6efe4d638823db00c70d6f359aa7b4416523142d17817

Observation 5eafd008-e32c-4673-8858-5012dbc16010 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.310124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.918736Z digest=sha256:91424b54da12beee7c4c03e42c3bbae60e87bb9792d5b11006193916141266bc

Observation 0bc467fe-6e33-4bce-91ca-c37e6abdde05 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.293025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.923474Z digest=sha256:baaffef95db15e83fb7dfdb08150b94cacd6af7231ddeeb103a07e42b226583a

Observation 9f6458c7-cc9f-462d-9cb0-9ea1c14b6cc5 · outbound

This paper cites Koukoulopoulos.

Bounds for moments of twisted quadratic characters of prime modulus Koukoulopoulos

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.277190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 71024932-6d71-4348-a95b-ae1b8a18d2fc · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 24

Resolution
unresolved
no resolver link, observed 2026-08-07T20:21:54.932939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T20:21:54.932939Z digest=sha256:dcd179cacea31265a6c4936889f9b8b5237f99b71ea1e0ad420ee52c107c863a

Observation bc3de5a2-4854-48a8-a7dc-d36d23324001 · outbound

This paper cites Munsch and Y.

Bounds for moments of twisted quadratic characters of prime modulus Munsch and Y

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.249773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.937975Z digest=sha256:90b8478a1cc74b5d660dd5c0203915b6f9299075f518ae8d30c1abe01a2455b7

Observation cd57318c-9cef-45ea-bc16-3b207e251253 · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.232581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 605ece8d-aa44-4fee-916f-8c8e24abd63d · outbound

This paper cites Soundararajan.

Bounds for moments of twisted quadratic characters of prime modulus Soundararajan

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T20:21:55.215647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.947737Z digest=sha256:0bbace5d8f7de841c628b5db0b5739f99a31825740abd87dc4e2d325bada8d6c

Observation 7b4796d8-0afa-4e1d-9384-2cdd84f5c8aa · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.199356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.952864Z digest=sha256:680bd9af102c95004a1f6972a725764e8f994e2b2614f2c5c962d3b47fd8972b

Observation e4411b7e-c1f7-42c1-aaad-b6d97b4c8c1d · outbound

This paper cites an unresolved cited work.

Bounds for moments of twisted quadratic characters of prime modulus Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T20:21:55.183200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-07T20:21:54.958029Z digest=sha256:fcc32be8350e82160e9d4bbb59311cd181888bc9641b924a5621ff8fe90e28c7

Pith citing papers

No inbound Pith citation observations are available.