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Paper Citation Record · LEDGER

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

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.039775Z digest=sha256:af460f332d815f30c7ca9af90071f29eeb2176109322b4606347e5f8659d8827

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.096486Z digest=sha256:27cf0f9bee10414673e5cb4c88c60b6c8f8ea8dd8ff926fe76c531032d97f232

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.165539Z digest=sha256:7af9b1ece1822f43f71058e8858048c0a67b59d27c685cd6c069f3020416db56

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.234211Z digest=sha256:44b4fb8f4bda0ae3a5f71bf1947903ba7de088b77fa76ec3d81f2be4a795277c

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.315915Z digest=sha256:4938bfdc46c4bc00a06fab992e02ff930943b13c0a7111b7e7ebf7fdbc25f864

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.388114Z digest=sha256:ec3a60468dc98a874e46cb36e2c3a2307d789e7e2f9ce0bf34233306e3dbf8db

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=sha256:9341ce8e688e1bf68748b949a0e148b351d95c293c4b511adf9e495aba360e7f

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=sha256:3a2aecc8c20129fb412e9cd59b7fdf76281d9c6a55bac35049a95b2d1420e179

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=sha256:63fe25391d8909c3dc8535bfcc8c5bc74538236b3ce916325d93b0cce57a6df0

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.707078Z digest=sha256:57dea1f3366433f6ee0c2155099ebadee0d307b51c2f13e7a93812ab50bf82ff

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.811333Z digest=sha256:b6d529e2b2b41e8a97fa7ab5918fdfb66ab4a7c464116ca947d21333908abba8

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.918632Z digest=sha256:64c18530578c9d7d0b6bda4c7bd75f70e8a864baa1cce4e7b40132e2bc64d28d

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:38.976267Z digest=sha256:d07cf619f58254d62e91a76e7b3f494e8bfe38ae112719fcb7d3d5e386ba1501

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:39.102930Z digest=sha256:6eba901457a4b765d0e75fa91435f8392e22451f46a6e763753fb6373fca202f

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T22:24:39.275092Z digest=sha256:6664757557ac16666d4c3feb72e489ed169ed4f41fdd2a00d443ba8d5280f8be

Pith citing papers

No inbound Pith citation observations are available.