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Paper Citation Record · LEDGER

Mean squares of quadratic twists of the Fourier coefficients of modular forms

As of 13 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2506.22256.

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

pith.paper-citation-record.v1
2506.22256 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:24:39.275092Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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 exact4
  • verified fuzzy5
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5c3ee970-245f-48d7-ab65-ffa44c4b9508 · outbound

This paper cites an unresolved cited work.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:24:42.326623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.039775Z digest=sha256:6f3905a4b0092c14be10875dd219e1f2170394a8e28e611e3466b997faf1eb3c

Observation 8a8c3e7d-3d81-4388-b1de-0f5ae5075952 · outbound

This paper cites Deligne, La conjecture de Weil.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Deligne, La conjecture de Weil

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:24:42.047687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.096486Z digest=sha256:40fe0e7a0ff0a333fb9a0370525fce827e3118ab8436784422f4768457de8bfd

Observation c81bfd13-2ef2-4b88-bd3b-c8e29228274b · outbound

This paper cites The mean square of real character sums.

Mean squares of quadratic twists of the Fourier coefficients of modular forms The mean square of real character sums

Reference 3

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:24:40.680268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.165539Z digest=sha256:c78c28971a3925790a777138a22d31677586d296d9b53ee3c64f49017d4bdd8a

Observation 96bb9e8c-0e8b-426d-97d4-d4874074ba2e · outbound

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

Mean squares of quadratic twists of the Fourier coefficients of modular forms Bounds for Moments of Twisted Fourier coefficients of Modular Forms

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:24:40.399363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.234211Z digest=sha256:eed5b7a08ba7f307af987ac5eb7f5ee3f7cfdefb59f6986bc461145ee382d009

Observation cd43e3df-da5d-4763-804d-f99561852f45 · outbound

This paper cites an unresolved cited work.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Unresolved cited work

Reference 5

Resolution
verified exact
raw_fallback, observed 2026-08-06T22:24:40.134967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.315915Z digest=sha256:25f25be09750cae6dc3132f532aaa2270afe5dc50bb5c8895904ab569ab8910c

Observation dcc1daa2-2049-4a94-9f0f-158eeb98da23 · outbound

This paper cites an unresolved cited work.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:24:41.817680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.388114Z digest=sha256:5821903e2075e8f4de40496834e95d2de54e56cd48c194d3e8aa5fc1594908d1

Observation f2a74a9a-7c15-4260-a4cc-a33e3ace8d21 · outbound

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

Mean squares of quadratic twists of the Fourier coefficients of modular forms Sharp conditional bounds for moments of the Riemann zeta function

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:38.485416Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:38.485416Z digest=sha256:c5aaca25439a3a728223b4c7fe0297e467bd74fc1dc1afe16491ef5fd22f59cb

Observation d8176ada-7b3d-4a05-9818-5608faf9df35 · outbound

This paper cites Iwaniec and E.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Iwaniec and E

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:38.558896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:38.558896Z digest=sha256:f93766836cd2ca761076db83059583e82d4cd3a1eabdc05686fa944ff53c3a90

Observation 371b231d-35b1-4624-b0ae-fcb2f894f8f6 · outbound

This paper cites an unresolved cited work.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Unresolved cited work

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:38.635322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:38.635322Z digest=sha256:e0bbe8a22036634d6b8cb58aae47625ff6e77e3625cf728bb88538af18b01543

Observation 9fdb42d5-4d16-4442-9ecd-2680e4abbe47 · outbound

This paper cites Munsch, Upper and lower bounds on moments of quadratic character sums and theta functions (Preprint).

Mean squares of quadratic twists of the Fourier coefficients of modular forms Munsch, Upper and lower bounds on moments of quadratic character sums and theta functions (Preprint)

Reference 10

Resolution
verified exact
raw_fallback, observed 2026-08-06T22:24:39.661553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.707078Z digest=sha256:46fdee9af97c0a65b5333e34dbe5fc9734d731cdaccf12683789a0113dc6774b

Observation 5bfb7d0f-ff74-43d5-a07b-0734677de4f8 · outbound

This paper cites Shimura, On the holomorphy of certain Dirichlet series , Proc.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Shimura, On the holomorphy of certain Dirichlet series , Proc

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:24:41.622941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.811333Z digest=sha256:b94af8716cf9e09452b4b3cc7b05151190f594b70f9119319521da4c260da779

Observation 5b1ca221-99cc-4f75-9bfd-1caf3c3aa5f3 · outbound

This paper cites Soundararajan, Nonvanishing of quadratic Dirichlet L-functions at s = 1 2 , Ann.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Soundararajan, Nonvanishing of quadratic Dirichlet L-functions at s = 1 2 , Ann

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:24:41.429549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.918632Z digest=sha256:e029ea39b629ccd115111499129cd2594f5b1ca87e91cd3f03c440bfbeeedcf2

Observation 802f27de-0bde-4822-b6ed-567259b35fa1 · outbound

This paper cites an unresolved cited work.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:24:41.225996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:38.976267Z digest=sha256:74a04504241b0511cac45023b0ac805ce95c3bc5befb0e2bcdae6d2bbc556690

Observation 0fbe6fae-5e44-4904-9083-b418b716e98c · outbound

This paper cites Soundararajan and M.

Mean squares of quadratic twists of the Fourier coefficients of modular forms Soundararajan and M

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:24:41.056858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:39.102930Z digest=sha256:a4c8628e6fde107c837b6eb9ed6c96f45262f459cf38a210f8dacef6fb25c4cf

Observation 70e4237a-f1df-4a55-bc19-1e5a489e0f6d · outbound

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

Mean squares of quadratic twists of the Fourier coefficients of modular forms Szab´ o,High moments of theta functions and character sums , Mathematika 70 (2024), no

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:24:40.878334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T22:24:39.275092Z digest=sha256:1da27b393ef24eacb725bac120ebd082016cb54d5e77a5178640d070120bc756

Pith citing papers

No inbound Pith citation observations are available.