Paper Citation Record · LEDGER

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus

As of 12 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2507.18186.

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

pith.paper-citation-record.v1
2507.18186 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:48:46.111077Z

measured 27 of 27 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:49:50.384076Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-11T10:56:02.989398Z

Reference resolution

25 of 25 outbound references displayed

verified exact3
verified fuzzy13
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f568d720-153b-4a17-b963-5fcb4a6dd403 · outbound

This paper cites On binary and quadratic divisor problems.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus On binary and quadratic divisor problems

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:48:46.705899Z

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 54f53bfb-e97f-4b74-8c04-ea98724286d1 · outbound

This paper cites Blomer, ´E.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Blomer, ´E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:50.842333Z

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 0de389f6-a83a-4440-a1cc-02b35509b978 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:50.635928Z

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 e2d39884-8a4e-4b44-974f-ccc797839db5 · outbound

This paper cites Blomer, ´E.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Blomer, ´E

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:50.468513Z

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 dc60e4c0-c49f-4fd6-84bd-b4db4ee36b3b · outbound

This paper cites Blomer and D.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Blomer and D

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:50.321494Z

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 6ff7b63b-1ff2-4f6f-a9f8-f7ac62c4c53b · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:50.081913Z

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 ff33911a-eb9f-41e3-8387-0de1ac45ff21 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:49.817363Z

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 1faeb868-38cd-4ac6-87a1-9218aa3545bb · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:49.583059Z

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 3e123daf-6b0a-4754-88d4-0e44d25b67d1 · outbound

This paper cites Gao and L.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Gao and L

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-06T14:48:46.572819Z

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 baef87cd-578f-4f65-ac35-c45c0dd77394 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:49.368590Z

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 1596b116-820f-46b0-a99b-8d6fea46f013 · outbound

This paper cites Hough, The angle of large values of L-functions, J.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Hough, The angle of large values of L-functions, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:49.081442Z

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 50fe8386-f11b-4d83-9064-a0b247bc6112 · outbound

This paper cites Iwaniec and E.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Iwaniec and E

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T14:48:44.624398Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd5ac929-e6b2-4ec2-bea5-f81b3d020a19 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:48.841444Z

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 3cc9e545-c3e9-4f6a-8b16-396435b92bbc · outbound

This paper cites Kowalski, P.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Kowalski, P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:48.524967Z

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 5ecd298c-eeec-4316-b8d8-e77c916c5261 · outbound

This paper cites Liu, Zeros and moments of L-functions and applications , 2024.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Liu, Zeros and moments of L-functions and applications , 2024

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:48.336519Z

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 a6e432a5-4d1b-48b1-bcaa-98048176d1b9 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:48.042579Z

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 d424ba6b-f0ce-4795-a3a0-39952c8f437f · outbound

This paper cites Munsch, Shifted moments of L-functions and moments of theta functions , Mathematika 63 (2017), no.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Munsch, Shifted moments of L-functions and moments of theta functions , Mathematika 63 (2017), no

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.905566Z

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 4f9a5005-7525-4583-b071-cc8d27b935bf · outbound

This paper cites Radziwi l l and K.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Radziwi l l and K

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.794155Z

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 60d348c3-425a-4d97-97ca-60899fb7c520 · outbound

This paper cites Rudnick and K.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Rudnick and K

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.638507Z

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 d71b1179-6bf6-48df-947a-29e8233eb84e · outbound

This paper cites Selberg, Contributions to the theory of Dirichlet’s L-functions, Skr.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Selberg, Contributions to the theory of Dirichlet’s L-functions, Skr

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.500758Z

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 23d707b0-1ab2-4f9b-bbaf-e430d3bbee68 · outbound

This paper cites Soundararajan, The fourth moment of Dirichlet L-functions, in: Analytic number theory, 239–246, Clay Math.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Soundararajan, The fourth moment of Dirichlet L-functions, in: Analytic number theory, 239–246, Clay Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.332268Z

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 3ce6a386-2eec-4909-a85e-3aa448967623 · outbound

This paper cites Szab´ o,High moments of theta functions and character sums , Mathematika 70 (2024), no.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Szab´ o,High moments of theta functions and character sums , Mathematika 70 (2024), no

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:47.175554Z

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 11a0def9-f4be-4408-a8d6-3a65b3b990f9 · outbound

This paper cites The fourth moment of Dirichlet $L$-functions at the central value.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus The fourth moment of Dirichlet $L$-functions at the central value

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:48:46.310414Z

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 b46d3b9a-1fbc-43a3-9fe4-dd757dc46140 · outbound

This paper cites an unresolved cited work.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:48:47.065295Z

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 1e12defb-3053-4292-a818-13e803fca84e · outbound

This paper cites Zacharias, Mollification of the fourth moment of Dirichlet L-functions, Acta Arith.

Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus Zacharias, Mollification of the fourth moment of Dirichlet L-functions, Acta Arith

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:48:46.850964Z

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

Observation 76a22122-65d2-4807-b05b-8ee392a30e92 · inbound

Simultaneous non-vanishing of Dirichlet L-functions cites this paper.

Simultaneous non-vanishing of Dirichlet L-functions Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-11T10:56:02.993589Z

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 9303ad15-d798-4d5e-8fd2-6489937b7e8a · inbound

On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect cites this paper.

On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect Twisted fourth moment of Dirichlet $L$-functions to a fixed modulus

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T04:49:50.384076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.