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Paper Citation Record · LEDGER

Fast multi-precision computation of some Euler products

As of 16 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:1908.06808.

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

pith.paper-citation-record.v1
1908.06808 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:44:29.799025Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

18 of 18 outbound references displayed

  • verified exact0
  • verified fuzzy12
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d36c3937-6a79-4252-8bb9-8d84c3268ec6 · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:30.170672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.683979Z digest=sha256:bae81dbb162b8b80c9d23fa61fcab68a92ec2430236bc85b791610eb924be950

Observation 74875f65-ca6e-4ea5-8156-a0f46481e15b · outbound

This paper cites R epresentation of integers by cyclotomic binary forms.

Fast multi-precision computation of some Euler products R epresentation of integers by cyclotomic binary forms

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.152012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 8053d5f2-d0d2-4311-9ff7-221559cd8c0e · outbound

This paper cites Gourdon and P.

Fast multi-precision computation of some Euler products Gourdon and P

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.130324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.698286Z digest=sha256:efcc1c105a75311aaae3e44a8eb4b15a2988518c1b1dc9f3b4eb6e4cb87bcd88

Observation 2d018199-b122-41a5-83de-4c403fd8c933 · outbound

This paper cites A classical introduction to modern number theory , vol- ume 84 of Graduate Texts in Mathematics.

Fast multi-precision computation of some Euler products A classical introduction to modern number theory , vol- ume 84 of Graduate Texts in Mathematics

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.114493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation cde76213-a0dc-4ac4-959f-77154b434705 · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:30.098596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.712673Z digest=sha256:07090cb00a04b2dd272993ec1331c69478d046b79534fcd6cd098f168e6a55a1

Observation 196e3206-7e65-413b-92dc-2c162fa099a9 · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:30.080473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.718995Z digest=sha256:5acb46f235974a4412f9e30bc78326432e008e90779a221311986a1c7e739626

Observation 80e8cb5a-dc6a-4bfa-8b8c-7d7a90ac7739 · outbound

This paper cites Moree and R.

Fast multi-precision computation of some Euler products Moree and R

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.060781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.726042Z digest=sha256:19238c5f6605022da196c87d535555a53d1444b81a1a9fc3936b55ce96ceb2e3

Observation 292216f5-6d9e-4b18-acd7-a71c4ae592f2 · outbound

This paper cites On the average number of elements in a finite field with order or index in a prescribed residue class.

Fast multi-precision computation of some Euler products On the average number of elements in a finite field with order or index in a prescribed residue class

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.039304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.731037Z digest=sha256:3b955e593cb45d5fcee8202413bc2570f77a623f4043f1e7826bd6275364af1d

Observation 93bb9a89-bafe-43e9-b8d8-79ae65298526 · outbound

This paper cites Zuckerman, and Hugh L.

Fast multi-precision computation of some Euler products Zuckerman, and Hugh L

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:30.019407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.735995Z digest=sha256:8e03468b67f502b5d11cfab3c6fff706f803e0267e56dc5e10b742939df05d0d

Observation 07f9b962-377b-4163-b943-c062721f016b · outbound

This paper cites The On-Line Encyclopedia of Integer Sequence , 2019.

Fast multi-precision computation of some Euler products The On-Line Encyclopedia of Integer Sequence , 2019

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.998496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.741013Z digest=sha256:7572ee2c29df32b24df54089cad1630c0485ebd220aa64580a4cb26e5673f51e

Observation a05ff75b-df33-4d49-871b-32802a004865 · outbound

This paper cites On the foundations of combinatorial t heory.

Fast multi-precision computation of some Euler products On the foundations of combinatorial t heory

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.979078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.750372Z digest=sha256:3045ca785e2f2bf923e42c5fd402fe02f5d6bbe8f792f384b42b27618c469556

Observation 808b3245-68e5-4d86-a6ca-d4d56493507c · outbound

This paper cites Le Math´ ematicien.

Fast multi-precision computation of some Euler products Le Math´ ematicien

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.960345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.755660Z digest=sha256:d8a445e3702f6234818461e76198c736e36c975fa36524d7a230841a1f0d56c5

Observation 4ca1bb0e-4956-498f-92f7-b0fa0197cefc · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:29.943251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.763549Z digest=sha256:ec5c6af93b78f132e2805ab626f8e073429e27bb9f829ecca29e172873b9bf0d

Observation 16ff6cee-0561-4bef-87da-39f8eb1d40ac · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:29.925377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.771678Z digest=sha256:60201025908ad23f8ac3c5f9ea73215f3ba4697502ccf3325cad6a11c8f46a6e

Observation d53b69f0-8a77-4efb-80f6-83fbce1635dd · outbound

This paper cites On the conjecture of Hardy & Littlewood c oncerning the number of primes of the form n2 ` a.

Fast multi-precision computation of some Euler products On the conjecture of Hardy & Littlewood c oncerning the number of primes of the form n2 ` a

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.908152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.778067Z digest=sha256:f07524216a8b2cf2f43cbe0bbe49992a802c883774cb204484af5e0ba1289895

Observation 65c684bd-dd83-42b3-ab45-dda5bfa7db45 · outbound

This paper cites On numbers of the form n4 ` 1.

Fast multi-precision computation of some Euler products On numbers of the form n4 ` 1

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.889956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.785115Z digest=sha256:689b85669ee6e27550f2d76676cb888845bc1685551d174fa7bb9845a95d8ab0

Observation 3f846a20-40e5-4837-b12f-aa7ad2105a0d · outbound

This paper cites Lal’s constant and generalizations.

Fast multi-precision computation of some Euler products Lal’s constant and generalizations

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:44:29.871636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T12:44:29.791463Z digest=sha256:035a2b3595ef0796448b99a4a4fdd66319ae1095cb070c2943c23cde7d574740

Observation 5922f32f-f5de-4d56-862e-2933ed3e486c · outbound

This paper cites an unresolved cited work.

Fast multi-precision computation of some Euler products Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:44:29.850126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Pith citing papers

No inbound Pith citation observations are available.