Paper Citation Record · LEDGER

Machine learning the vanishing order of rational L-functions

As of 9 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2502.10360.

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

pith.paper-citation-record.v1
2502.10360 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T18:32:14.648571Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:28:19.727682Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T05:28:20.032556Z

Reference resolution

35 of 35 outbound references displayed

verified exact1
verified fuzzy19
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0c3294a8-0d86-4430-a55a-5cc149851786 · outbound

This paper cites Machine-learning of the class number of real quadratic fields.

Machine learning the vanishing order of rational L-functions Machine-learning of the class number of real quadratic fields

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:15.207049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c9c82027-2ac3-4601-a6fa-0c06a9947620 · outbound

This paper cites Best, Jonathan Bober, Andrew R.

Machine learning the vanishing order of rational L-functions Best, Jonathan Bober, Andrew R

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:15.186981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6009a76d-acfa-4d90-9f5e-d209f69af4c5 · outbound

This paper cites Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein.

Machine learning the vanishing order of rational L-functions Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:15.170360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5f7c3ae5-d585-4ec0-9061-f7050ea8d0d4 · outbound

This paper cites Booker, Jeroen Sijsling, Andrew V.

Machine learning the vanishing order of rational L-functions Booker, Jeroen Sijsling, Andrew V

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:15.151962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e0477ce9-eeb3-4462-8fd2-49b6907a904c · outbound

This paper cites Rational L -functions in LMFDB with root analytic conductor less than 4.

Machine learning the vanishing order of rational L-functions Rational L -functions in LMFDB with root analytic conductor less than 4

Reference 6

Resolution: verified exact; doi, observed 2026-08-07T18:32:14.701419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bca93567-60c9-494e-8eed-e6e09d1ef0f3 · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:15.126313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0512a67b-f5a7-4831-883e-c5b9b87f85c0 · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:15.100642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fd24ef1b-487a-4f08-8469-664eafcb2973 · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:15.080678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 17519d87-2476-4a31-af90-6a67a8abae3d · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:15.066490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d654c164-3356-44c3-9bb9-0537430e645b · outbound

This paper cites A database of H ilbert modular forms.

Machine learning the vanishing order of rational L-functions A database of H ilbert modular forms

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:15.051592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 13283a72-9688-499c-961d-19300584ef4d · outbound

This paper cites Machine-learning number fields.

Machine learning the vanishing order of rational L-functions Machine-learning number fields

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.139935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 738ba1ca-b7a8-416a-9418-ddebadbac6c0 · outbound

This paper cites Machine-learning the S ato- T ate conjecture.

Machine learning the vanishing order of rational L-functions Machine-learning the S ato- T ate conjecture

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.160737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b0757ff-8d35-4c5a-b12b-5962b7eb5064 · outbound

This paper cites Machine learning invariants of arithmetic curves.

Machine learning the vanishing order of rational L-functions Machine learning invariants of arithmetic curves

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.166165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2676a44-c1e6-4f9c-8a6c-89da439272d5 · outbound

This paper cites Murmurations of elliptic curves.

Machine learning the vanishing order of rational L-functions Murmurations of elliptic curves

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.202256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 791a3834-1070-458c-856b-e613437cc5f7 · outbound

This paper cites Jones and David P.

Machine learning the vanishing order of rational L-functions Jones and David P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.992354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a5536ebe-e539-4e82-a26a-490803600a9a · outbound

This paper cites Ranks of elliptic curves and deep neural networks.

Machine learning the vanishing order of rational L-functions Ranks of elliptic curves and deep neural networks

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.216847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88d706bb-40aa-4ef9-81cf-50c304d8d0b0 · outbound

This paper cites UpSet : visualization of intersecting sets.

Machine learning the vanishing order of rational L-functions UpSet : visualization of intersecting sets

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.972732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e496f954-5a17-4b73-a139-466de99d5bd9 · outbound

This paper cites The L -functions and modular forms database.

Machine learning the vanishing order of rational L-functions The L -functions and modular forms database

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.961427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1aa589cb-9847-4b0c-a9e4-01ce3bae8d43 · outbound

This paper cites Murmurations of D irichlet C haracters.

Machine learning the vanishing order of rational L-functions Murmurations of D irichlet C haracters

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.948902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1cf7f388-ebad-47d9-810e-1319a9302c18 · outbound

This paper cites Machine learning for number theory: unsupervised learning with L -functions.

Machine learning the vanishing order of rational L-functions Machine learning for number theory: unsupervised learning with L -functions

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.930888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 12b84fbd-a1c4-4e92-8ee1-740e6a243b4b · outbound

This paper cites Letter to sutherland and zubrilina.

Machine learning the vanishing order of rational L-functions Letter to sutherland and zubrilina

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.914988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a3bd869a-966b-4eab-abce-923d8db1805b · outbound

This paper cites Old and new conjectures and results about a class of D irichlet series.

Machine learning the vanishing order of rational L-functions Old and new conjectures and results about a class of D irichlet series

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.900753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a1acbcfc-4a9a-4425-b1e4-bdfb8974445e · outbound

This paper cites Letter from sutherland to rubinstein and sarnak.

Machine learning the vanishing order of rational L-functions Letter from sutherland to rubinstein and sarnak

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.886411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f0ab00eb-a2fc-45d8-85d3-252774d2ff45 · outbound

This paper cites Modular forms and elliptic curves over imaginary quadratic number fields.

Machine learning the vanishing order of rational L-functions Modular forms and elliptic curves over imaginary quadratic number fields

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.873446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1e2d1b39-fa91-4ec9-aafc-1e696b3b7e5f · outbound

This paper cites Amir, Y.-H.

Machine learning the vanishing order of rational L-functions Amir, Y.-H

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.861740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fe0e8ec0-6bd1-4efe-a1c0-195565fd3183 · outbound

This paper cites Murmurations of Mestre-Nagao sums.

Machine learning the vanishing order of rational L-functions Murmurations of Mestre-Nagao sums

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.471630Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9885c16a-2fac-4c05-98cc-82ce38314678 · outbound

This paper cites He, K.-H.

Machine learning the vanishing order of rational L-functions He, K.-H

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.846017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 38742fd3-e197-4f4a-8401-a868ab3905d6 · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:14.830069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 82b98c00-6a7e-48cb-ac21-1fb8b381b702 · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:14.811691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9cf841f0-851e-432d-8462-e80c13fe2221 · outbound

This paper cites He, K.-H.

Machine learning the vanishing order of rational L-functions He, K.-H

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.790963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 917cbd65-5f96-4488-aa43-7a57dddc0e1a · outbound

This paper cites Oliver, Machine Learning for Number Theory: Unsupervised Learning with L-Functions , International Congress on Mathematical Software (2024), 196--203.

Machine learning the vanishing order of rational L-functions Oliver, Machine Learning for Number Theory: Unsupervised Learning with L-Functions , International Congress on Mathematical Software (2024), 196--203

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.777221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a832e914-7403-476a-adb5-44b17fb38873 · outbound

This paper cites Selberg Old and new conjectures and results about a class of Dirichlet series , Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Salerno: Univ.

Machine learning the vanishing order of rational L-functions Selberg Old and new conjectures and results about a class of Dirichlet series , Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Salerno: Univ

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.762075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cdf3466b-2313-429e-9236-582606c53f0c · outbound

This paper cites Kazalicki and D.

Machine learning the vanishing order of rational L-functions Kazalicki and D

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.597014Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fb3a959-3257-4085-b343-e6634c728a6b · outbound

This paper cites an unresolved cited work.

Machine learning the vanishing order of rational L-functions Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:14.748374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ff59471f-2919-44ce-b99a-c3e9309bec84 · outbound

This paper cites Predicting root numbers with neural networks.

Machine learning the vanishing order of rational L-functions Predicting root numbers with neural networks

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.648571Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation b31b20b7-fda9-4f1d-9db0-a5607fb6f52e · inbound

Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums cites this paper.

Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums Machine learning the vanishing order of rational L-functions

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:28:20.037679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.