Paper Citation Record · LEDGER

Real exponential sums over primes and prime gaps

As of 12 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2307.08725.

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

pith.paper-citation-record.v1
2307.08725 v4

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T07:21:33.729754Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

19 of 19 outbound references displayed

verified exact0
verified fuzzy13
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 94895c4b-cd2b-4438-b439-74b2856b02ca · outbound

This paper cites Algorithmic Number Theory, Volume 1: Eﬃcient Algorithms.

Real exponential sums over primes and prime gaps Algorithmic Number Theory, Volume 1: Eﬃcient Algorithms

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.334776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c0108168-2921-4cdc-816c-0819a7f70777 · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.328417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2ab62f67-9634-4838-a529-bd2c16c22b45 · outbound

This paper cites Erd˝ os.Beweis eines Satzes von Tschebyschef.

Real exponential sums over primes and prime gaps Erd˝ os.Beweis eines Satzes von Tschebyschef

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.325345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0338fa19-3f05-4cac-b222-b4e7491b9812 · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.321877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 891fdf87-f2b0-4a0c-b47f-eb484c9105b8 · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.331354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7ba5b9a4-a938-4a87-b4ad-f5d82c1046ae · outbound

This paper cites Introduction to Number Theory.

Real exponential sums over primes and prime gaps Introduction to Number Theory

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.318329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8a5c06a7-e803-4e72-b7bc-7ff77dd46e2d · outbound

This paper cites Abstract Analytic Number Theory.

Real exponential sums over primes and prime gaps Abstract Analytic Number Theory

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.338573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0d1aa1ae-1c68-4a44-ac1e-d322cdbb60fc · outbound

This paper cites Analytic Number Theory - Exploring the Anatomy of the Intege rs.

Real exponential sums over primes and prime gaps Analytic Number Theory - Exploring the Anatomy of the Intege rs

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.366480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7222a8dc-1918-4905-baa7-d1f22803ee31 · outbound

This paper cites Complex Analysis.

Real exponential sums over primes and prime gaps Complex Analysis

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.369782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 64ccfb24-6eb1-4d72-95e9-8691fa9f50d4 · outbound

This paper cites Primes in short intervals.

Real exponential sums over primes and prime gaps Primes in short intervals

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.373566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 447d7ca9-03d8-46cd-bc92-f8cf427fb642 · outbound

This paper cites Montgomery.

Real exponential sums over primes and prime gaps Montgomery

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.376956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0bcb76b2-125a-45b6-a284-cd207814de82 · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.380373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation df9ccda8-2b3f-4677-be5e-5fd33421468c · outbound

This paper cites The prime number theorem: Analytic and elementary proofs.

Real exponential sums over primes and prime gaps The prime number theorem: Analytic and elementary proofs

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.356604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 42b3a14f-f771-494e-a9de-5540deeecd03 · outbound

This paper cites N´ umeros primos: mist´ erios e recordes.

Real exponential sums over primes and prime gaps N´ umeros primos: mist´ erios e recordes

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.363079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 19b15ee4-07e4-467d-a447-c2d17a017c11 · outbound

This paper cites Barkley Rosser; Lowell Schoenfeld.

Real exponential sums over primes and prime gaps Barkley Rosser; Lowell Schoenfeld

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.349295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 542de187-a94d-44c0-9d57-9d6392e0f423 · outbound

This paper cites Acta Fac.

Real exponential sums over primes and prime gaps Acta Fac

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.341985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 829773d6-93a0-4e61-afcb-32e1b6e97d07 · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.345693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 28db9b23-cfb6-4c4b-8a0a-8a7650c4b2a3 · outbound

This paper cites Sutherland.

Real exponential sums over primes and prime gaps Sutherland

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T07:24:07.353266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 894bd225-14df-4ee3-93b8-16b8f4ff656c · outbound

This paper cites an unresolved cited work.

Real exponential sums over primes and prime gaps Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-05-24T07:24:07.359743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.