Paper Citation Record · LEDGER

On Murmurations and Trace Formulas

As of 8 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2506.01640.

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

pith.paper-citation-record.v1
2506.01640 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:42:31.931969Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T10:03:12.944307Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T10:04:06.249554Z

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy18
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f920ac01-b5d5-4166-9386-d1fb584c0f27 · outbound

This paper cites Booker, Min Lee, and David Lowry-Duda.

On Murmurations and Trace Formulas Booker, Min Lee, and David Lowry-Duda

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.764477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1aed786-e1d4-4075-ad1b-73877d34bd8c · outbound

This paper cites Booker, Min Lee, David Lowry-Duda, Andrei Seymour-Howell, and Nina Zubrilina.

On Murmurations and Trace Formulas Booker, Min Lee, David Lowry-Duda, Andrei Seymour-Howell, and Nina Zubrilina

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:33.107261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fb460c9b-8cc1-4c7f-b21e-847f71847846 · outbound

This paper cites Farmer, and Martin R.

On Murmurations and Trace Formulas Farmer, and Martin R

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:33.037644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cfb90bf0-d266-4ff6-9aba-c28da3469a75 · outbound

This paper cites Twist-minimal trace formula for holomorphic cusp forms.

On Murmurations and Trace Formulas Twist-minimal trace formula for holomorphic cusp forms

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.993807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ede49ab1-31f1-419c-8e38-7c3b7f86939c · outbound

This paper cites Murmurations and ratios conjectures.

On Murmurations and Trace Formulas Murmurations and ratios conjectures

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.829521Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3db8ac14-d87d-4b4e-ba0f-af9f6df3e8a8 · outbound

This paper cites an unresolved cited work.

On Murmurations and Trace Formulas Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.833585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7eebf0e8-3a24-400f-a550-0f377a162474 · outbound

This paper cites Murmurations of elliptic curves.

On Murmurations and Trace Formulas Murmurations of elliptic curves

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.947200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ce4ea800-e4ba-4d6e-b1af-06be1f2cc2d1 · outbound

This paper cites Analytic number theory , volume 53 of American Mathematical Society Colloquium Publications.

On Murmurations and Trace Formulas Analytic number theory , volume 53 of American Mathematical Society Colloquium Publications

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.844767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 211f5ec4-7145-4755-8a8c-1156007f6ca9 · outbound

This paper cites Low lying zeros of families of L -functions.

On Murmurations and Trace Formulas Low lying zeros of families of L -functions

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.848430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9eef299c-a7c9-41cf-a31d-a6f3645b031e · outbound

This paper cites an unresolved cited work.

On Murmurations and Trace Formulas Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:42:32.890951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 65f34c05-6e6a-40ef-961f-3b5c0d2b0dd9 · outbound

This paper cites Random matrices, Frobenius eigenvalues, and monodromy , volume 45.

On Murmurations and Trace Formulas Random matrices, Frobenius eigenvalues, and monodromy , volume 45

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.830503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9cfc7b16-f040-4bd2-a890-9f0394dcab6d · outbound

This paper cites Katz and Peter Sarnak.

On Murmurations and Trace Formulas Katz and Peter Sarnak

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.751063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c8d50511-4e5a-4e38-834a-67b64eae6685 · outbound

This paper cites Murmurations in M aass forms.

On Murmurations and Trace Formulas Murmurations in M aass forms

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.704769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a5d4baee-1c78-4101-a50d-8192b62be007 · outbound

This paper cites On murmurations and trace formulas.

On Murmurations and Trace Formulas On murmurations and trace formulas

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.660913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 662cd52f-83a1-4057-92ed-f7e974812fbd · outbound

This paper cites Murmurations of D irichlet characters.

On Murmurations and Trace Formulas Murmurations of D irichlet characters

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.617176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 17f3c2f6-9e11-429e-8b02-471fd88d2594 · outbound

This paper cites Root number bias for newforms.

On Murmurations and Trace Formulas Root number bias for newforms

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.559515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d36bf7a8-87b7-4751-8fc5-258d4748092b · outbound

This paper cites Variations on murmurations.

On Murmurations and Trace Formulas Variations on murmurations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.883148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b372d17-2a2f-4abe-bad4-fd376b06e7fd · outbound

This paper cites \" U ber die E ntwicklungskoeffizienten der automorphen F ormen.

On Murmurations and Trace Formulas \" U ber die E ntwicklungskoeffizienten der automorphen F ormen

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.509220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation af9c2414-b5a9-47d0-a49b-c6e7fa524b0e · outbound

This paper cites Letter to D rew S utherland and N ina Z ubrilina on murmurations and root numbers.

On Murmurations and Trace Formulas Letter to D rew S utherland and N ina Z ubrilina on murmurations and root numbers

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.454921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f7c2431c-1d19-4e70-8b2d-38bbcab30be6 · outbound

This paper cites Rigorous computation of Maass cusp forms.

On Murmurations and Trace Formulas Rigorous computation of Maass cusp forms

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.406864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a04b14c3-9eb3-4eae-87c9-a94778d50d8e · outbound

This paper cites On modular forms of half integral weight.

On Murmurations and Trace Formulas On modular forms of half integral weight

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.351783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b09d4fa8-4459-4f59-bd87-e19ba68cdd89 · outbound

This paper cites Sutherland.

On Murmurations and Trace Formulas Sutherland

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.900564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d4807f8-1f59-4738-9b1a-ff5835ea8f9c · outbound

This paper cites Explicit trace formula for Hecke operators.

On Murmurations and Trace Formulas Explicit trace formula for Hecke operators

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.282398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2743418b-5b0f-4cbb-b4ff-78bedbc817bb · outbound

This paper cites Murmurations of arithmetic l -functions.

On Murmurations and Trace Formulas Murmurations of arithmetic l -functions

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.229131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6085009d-4060-43bd-b9e3-475585774047 · outbound

This paper cites Jacobi forms and a certain space of modular forms.

On Murmurations and Trace Formulas Jacobi forms and a certain space of modular forms

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.185664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4b95a4ec-e8c0-4fad-91e0-577804c4c4d8 · outbound

This paper cites Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields.

On Murmurations and Trace Formulas Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.918552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69aaf442-db56-424d-b9cd-ee2755adb5a2 · outbound

This paper cites On the traces of H ecke operators for a normalizer of 0 (N).

On Murmurations and Trace Formulas On the traces of H ecke operators for a normalizer of 0 (N)

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:42:32.131411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3a830d5c-dfc8-486a-9356-f74218b5b116 · outbound

This paper cites Murmurations.

On Murmurations and Trace Formulas Murmurations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T11:42:31.931969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation e2d38d52-954c-4367-babb-6dfa14aa724c · inbound

Computer vision and converse theorems cites this paper.

Computer vision and converse theorems On Murmurations and Trace Formulas

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-10T10:04:06.251955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.