Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-28T08:32:26.456964Z
Paper Citation Record · LEDGER
Pair correlation of $\alpha n^{\theta}$ for random $\theta$
As of 20 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2606.03781.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
37 of 37 outbound references displayed
- verified exact5
- verified fuzzy0
- unresolved32
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 927a7b44-66d0-49b0-a2ad-63efee2415f5 · outbound
This paper cites Aistleitner, S.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, S
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 74f937bc-6873-4e16-9eae-76052ed0ff27 · outbound
This paper cites Aistleitner, D.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, D
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1f946036-6e13-4949-9a6f-efaf5c6dfc34 · outbound
This paper cites Aistleitner, T.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, T
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b05660d9-420d-43a9-bf6b-d2d19a610728 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 89dcc799-f18a-4e32-9483-9f3cb74b9ac3 · outbound
This paper cites Bourgain.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Bourgain
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 083291d9-2302-4017-98bb-b9810c492119 · outbound
This paper cites Browning and I.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Browning and I
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b5162366-1aba-482e-b4be-5fdf9a97ad85 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ee924862-d719-4dce-ad2b-f8e5d0ed7c75 · outbound
This paper cites El-Baz, J.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ El-Baz, J
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5f480fa8-1218-4dc5-9ec9-aa5c2a015082 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a45dc820-e469-4c42-b8fb-cf22e9d489b0 · outbound
This paper cites Grepstad and G.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Grepstad and G
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9c371275-79a2-4448-bb18-3a806d179a57 · outbound
This paper cites The bad and rough rotation is Poissonian.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ The bad and rough rotation is Poissonian
Reference 11
- Resolution
- verified exact
- arxiv_id, observed 2026-08-17T01:12:46.828665Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9b2be9fe-8e36-4054-b2cc-05e733803589 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 07eb9059-3c7c-48f9-8ff0-4a3e5b52290a · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 38ca3895-1ecd-4db3-b030-a3c482905279 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4931ffdf-b9d2-416a-92a1-7275fccbe81f · outbound
This paper cites Iwaniec and E.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Iwaniec and E
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0583a536-c8ea-4398-a3ca-4b4264c4c5a6 · outbound
This paper cites Metric Poissonian pair correlation for real sequences and energy estimates.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Metric Poissonian pair correlation for real sequences and energy estimates
Reference 16
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T05:06:40.080828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4640c115-1cda-4067-98ff-5da4ea4aa6c7 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7da622d9-9718-4389-b025-3c073252b0bf · outbound
This paper cites Kuipers and H.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Kuipers and H
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5e668ad5-8252-49cd-a16f-82bb0f244940 · outbound
This paper cites Larcher and W.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Larcher and W
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2ab05f22-c972-4ab8-9d3c-858c3004485b · outbound
This paper cites Poissonian correlations of $\alpha n^d$ mod $1$.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Poissonian correlations of $\alpha n^d$ mod $1$
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-07-02T05:06:40.070003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a961bde4-3015-45aa-823f-6f12fd394749 · outbound
This paper cites Lutsko, A.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko, A
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6b9fa3bd-4379-45aa-ad5a-ff633519908d · outbound
This paper cites Lutsko and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko and N
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 31eec1a4-1cff-4536-848f-8b2d38618093 · outbound
This paper cites Lutsko and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko and N
Reference 23
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b2e27f56-6204-4332-b90d-63a46bf6fd13 · outbound
This paper cites Marklof and A.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Marklof and A
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 90c9e04c-12a2-4b50-b04f-07cbd2ac7855 · outbound
This paper cites Radziwi l l and A.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Radziwi l l and A
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6690d383-e8c6-4e58-8b3c-bbff083b11ec · outbound
This paper cites Radziwi l l and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Radziwi l l and N
Reference 26
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T05:06:40.072423Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e6b0209a-c896-4fdf-913f-9c025030a21a · outbound
This paper cites Robert and P.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Robert and P
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation db649e6a-ad86-47fa-8ad5-c9db37bd440c · outbound
This paper cites Rudnick and P.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and P
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6effc9af-3be7-4675-b20b-efdd68563a2c · outbound
This paper cites Rudnick, P.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick, P
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59ccb2f2-66c0-47aa-ba0f-a9f85a4c20b4 · outbound
This paper cites Rudnick and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and N
Reference 30
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8947245c-d87f-4b8e-a7bc-47105d65e7c9 · outbound
This paper cites Rudnick and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and N
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e42c460-c5a8-4e05-b284-6f28d7c66cb6 · outbound
This paper cites Rudnick and A.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and A
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 45a6a296-8810-42c7-926b-76834712f3bc · outbound
This paper cites New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
Reference 33
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T05:06:40.077483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 21ddbe07-9b08-42f3-9328-fa08c2e0a94c · outbound
This paper cites Technau and N.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Technau and N
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b7f6a176-2da5-424e-bf38-c6f661a9ec47 · outbound
This paper cites Tenenbaum.Introduction ` a la th´ eorie analytique et probabiliste des nombres.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Tenenbaum.Introduction ` a la th´ eorie analytique et probabiliste des nombres
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 97566031-c211-40fa-9482-157809eb2837 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1620732a-d62c-47ae-9402-e1ed43d6fa77 · outbound
This paper cites an unresolved cited work.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work
Reference 37
- Resolution
- unresolved
- no resolver link, observed 2026-06-28T08:32:26.456964Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.