Paper Citation Record · LEDGER

Pointwise convergence of polynomial multiple ergodic averages along the primes

As of 13 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 1 inbound Pith citation observation for arXiv:2505.15549.

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

pith.paper-citation-record.v1
2505.15549 v2

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:22:14.048302Z

measured 59 of 59 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:36:56.808600Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

58 of 58 outbound references displayed

verified exact1
verified fuzzy47
unresolved10
parse uncertain0
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External citation measurements

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Outbound references

Observation 4a8da8b2-62a0-4fde-a31c-ba7589c51b50 · outbound

This paper cites Austin, On the norm convergence of non-conventional ergodic averages, Ergodic Theory Dynam.

Pointwise convergence of polynomial multiple ergodic averages along the primes Austin, On the norm convergence of non-conventional ergodic averages, Ergodic Theory Dynam

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:24.064428Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0db87239-6e6c-4658-b79c-e28d43538634 · outbound

This paper cites Bergelson, Ergodic Ramsey Theory – an update, Ergodic Theory of Zd-actions (edited by M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bergelson, Ergodic Ramsey Theory – an update, Ergodic Theory of Zd-actions (edited by M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.934144Z

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Observation 6e2a7291-0b10-4daf-a41a-85425ad8ca1f · outbound

This paper cites Bergelson, A.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bergelson, A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.854560Z

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Observation ec9be497-b4eb-49e0-a800-69a46e7e8421 · outbound

This paper cites Bergelson, Combinatorial and Diophantine Applications of Ergodic Theory (with appendices by A.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bergelson, Combinatorial and Diophantine Applications of Ergodic Theory (with appendices by A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.717092Z

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Observation f50d1da4-8474-4132-a7f6-3ee58ee07494 · outbound

This paper cites Birkhoff, Proof of the ergodic theorem, Proc.

Pointwise convergence of polynomial multiple ergodic averages along the primes Birkhoff, Proof of the ergodic theorem, Proc

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.551761Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c68b4bbe-4ce1-4a57-a655-d90d1457438e · outbound

This paper cites Bourgain, Double recurrence and almost sure convergence, J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bourgain, Double recurrence and almost sure convergence, J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.370318Z

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Observation e4d1662e-3f8d-4dc2-a522-77b0377f08a3 · outbound

This paper cites Bourgain, Pointwise ergodic theorems for arithmetic sets, Inst.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bourgain, Pointwise ergodic theorems for arithmetic sets, Inst

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.171632Z

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Observation 03a2e6ec-af9b-4b31-9ae3-6d53292c4384 · outbound

This paper cites Bourgain, An approach to pointwise ergodic theorems, Geometric aspects of functional analysis (1986/87), Lecture Notes in Math., 317, 204–223.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bourgain, An approach to pointwise ergodic theorems, Geometric aspects of functional analysis (1986/87), Lecture Notes in Math., 317, 204–223

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:23.038224Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5d0029d8-fc95-477c-80df-c60ee2814e60 · outbound

This paper cites Bourgain, M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bourgain, M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:22.935994Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 46d3e2aa-d457-4d6d-9308-3fde5cb1434c · outbound

This paper cites Bruhat, Distributions sur un groupe localement compact et applications ` a l’´ etude des repr´ esentations des groupes ℘-adiques, Bull.

Pointwise convergence of polynomial multiple ergodic averages along the primes Bruhat, Distributions sur un groupe localement compact et applications ` a l’´ etude des repr´ esentations des groupes ℘-adiques, Bull

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:22.823617Z

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Observation e77f01f0-4fc8-4f9c-96db-443237bce774 · outbound

This paper cites Calder´ on, Ergodic theory and translation invariant operators, Proc.

Pointwise convergence of polynomial multiple ergodic averages along the primes Calder´ on, Ergodic theory and translation invariant operators, Proc

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:22.726017Z

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Observation a33f7e14-ba2c-4ec8-ac0a-2cd649be6a77 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:22.573244Z

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Observation 03d1b0bd-8d55-4601-8152-0b0e08935a1e · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:22.401734Z

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Observation 7b3534a4-6eef-40e6-8983-f07feabab189 · outbound

This paper cites Duoandikoetxea, J.L.

Pointwise convergence of polynomial multiple ergodic averages along the primes Duoandikoetxea, J.L

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:22.225941Z

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Observation 633f73a9-e212-4a67-987f-23ebbaa771b3 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:22.036550Z

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Observation 4f072604-515c-4149-a2c5-3d07d3722cc9 · outbound

This paper cites Frantzikinakis, Some open problems on multiple ergodic averages, Bull.

Pointwise convergence of polynomial multiple ergodic averages along the primes Frantzikinakis, Some open problems on multiple ergodic averages, Bull

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:21.819750Z

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Observation 8e5cd41d-5f38-4c10-bc55-15dbda61f6fc · outbound

This paper cites Frantzikinakis, B.

Pointwise convergence of polynomial multiple ergodic averages along the primes Frantzikinakis, B

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:21.603364Z

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Observation 85ad193e-0f3c-4e08-a270-c223700db714 · outbound

This paper cites Frantzikinakis, B.

Pointwise convergence of polynomial multiple ergodic averages along the primes Frantzikinakis, B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:21.387435Z

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Observation e3d78727-0998-4d4d-9753-3f7dfbee1308 · outbound

This paper cites Frantzikinakis, B.

Pointwise convergence of polynomial multiple ergodic averages along the primes Frantzikinakis, B

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:21.196250Z

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Observation 50ed1cfd-e987-49bb-9f5a-2d24fe99ed07 · outbound

This paper cites Furstenberg.

Pointwise convergence of polynomial multiple ergodic averages along the primes Furstenberg

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:21.003999Z

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Observation 6b0ba81b-d5c8-45e2-9395-abd53c83ebaf · outbound

This paper cites Grafakos, Classical Fourier Analysis, third edition, Graduate Texts in Mathematics, vol.

Pointwise convergence of polynomial multiple ergodic averages along the primes Grafakos, Classical Fourier Analysis, third edition, Graduate Texts in Mathematics, vol

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:20.883977Z

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Observation 9ef43ec9-5d8a-4785-a18e-a7393af77ade · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:20.674793Z

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Observation 845d04c9-a417-421c-aa48-6760de4dd5ea · outbound

This paper cites Green, T.

Pointwise convergence of polynomial multiple ergodic averages along the primes Green, T

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:20.429002Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 44725fe1-43ae-4a22-8bac-622b77168d62 · outbound

This paper cites Host, Ergodic seminorms for commuting transformations and applications, Studia Math.

Pointwise convergence of polynomial multiple ergodic averages along the primes Host, Ergodic seminorms for commuting transformations and applications, Studia Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:20.260320Z

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Observation 40f8c764-c352-4085-967d-bd8ec0193b45 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:20.162101Z

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Observation 7ccc096c-0bd3-4b7e-83ee-bd639f5e04fc · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:20.064107Z

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Observation 53566606-7b60-4e82-a5e7-5e3b62664cdf · outbound

This paper cites Ionescu, S.

Pointwise convergence of polynomial multiple ergodic averages along the primes Ionescu, S

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.937137Z

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Observation 5d74d96e-f754-487c-afd1-28cda5569555 · outbound

This paper cites Iwaniec, E.

Pointwise convergence of polynomial multiple ergodic averages along the primes Iwaniec, E

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.694607Z

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Observation ef29e3d3-dd4a-4640-b9a3-d4efffef6fc9 · outbound

This paper cites Kosz, Sharp constants in inequalities admitting the Calder´ on transference principle, Ergodic Theory Dynam.

Pointwise convergence of polynomial multiple ergodic averages along the primes Kosz, Sharp constants in inequalities admitting the Calder´ on transference principle, Ergodic Theory Dynam

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.482837Z

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Observation ae24fb5f-e2c8-4eb9-b84d-9d2ef58100a1 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T15:22:10.220257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7111d825-6990-477d-9a20-70199a902f2b · outbound

This paper cites Krause, M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Krause, M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.367147Z

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Observation 6757a862-05df-40f6-8397-6712f6a568e7 · outbound

This paper cites Krause, H.

Pointwise convergence of polynomial multiple ergodic averages along the primes Krause, H

Reference 32

Resolution: verified exact; raw_fallback, observed 2026-08-07T15:22:14.435198Z

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Observation a269cc25-bae4-4e43-a134-508727563eab · outbound

This paper cites Leibman, Convergence of multiple ergodic averages along polynomials of several variables, Israel J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Leibman, Convergence of multiple ergodic averages along polynomials of several variables, Israel J

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.195587Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7cc611ba-61b3-45dc-91ef-4e2042a891ab · outbound

This paper cites L´ epingle, La variation d’ordre p des semi-martingales, Z.

Pointwise convergence of polynomial multiple ergodic averages along the primes L´ epingle, La variation d’ordre p des semi-martingales, Z

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:19.081091Z

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Observation dcd1125c-295d-4e63-89e8-bbbf3133b8c4 · outbound

This paper cites Matom¨ aki, X.

Pointwise convergence of polynomial multiple ergodic averages along the primes Matom¨ aki, X

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.956558Z

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Observation 7ac2cc88-ad34-4950-b566-3ce4cd1ac0ea · outbound

This paper cites Matom¨ aki, X.

Pointwise convergence of polynomial multiple ergodic averages along the primes Matom¨ aki, X

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.767519Z

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Observation b1ce4a89-35d3-4030-ac2c-221178d8aa80 · outbound

This paper cites Mehlhop, W.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mehlhop, W

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.569307Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 273f30f4-0d52-4a5c-8314-bee4324b6c16 · outbound

This paper cites Mirek, Square function estimates for discrete Radon transforms, Anal.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mirek, Square function estimates for discrete Radon transforms, Anal

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.430696Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cd5184d7-33e5-4969-9ed9-f428acc44836 · outbound

This paper cites Mirek, E.M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mirek, E.M

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.344812Z

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Observation 3134778c-a32c-4340-9b8e-5e23683f63a5 · outbound

This paper cites Mirek, E.M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mirek, E.M

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.159686Z

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Observation 033f9032-94cb-4d33-9062-00bcca188793 · outbound

This paper cites Mirek, B.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mirek, B

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:18.039029Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 602f2b71-db1a-4473-88b3-5f3ebb586f41 · outbound

This paper cites Mirek, E.M.

Pointwise convergence of polynomial multiple ergodic averages along the primes Mirek, E.M

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:17.844287Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b6b83f5f-bfd6-4285-bee1-47b7df74de02 · outbound

This paper cites Nair, On polynomials in primes and J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Nair, On polynomials in primes and J

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:17.640290Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cb0d1dce-f5c4-4d4d-84b4-5519b2160a16 · outbound

This paper cites Nair, On polynomials in primes and J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Nair, On polynomials in primes and J

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:17.486156Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 349267ee-c6cf-4181-b56a-fefe4dc0f316 · outbound

This paper cites von Neumann, Proof of the quasi-ergodic hypothesis, Proc.

Pointwise convergence of polynomial multiple ergodic averages along the primes von Neumann, Proof of the quasi-ergodic hypothesis, Proc

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:17.261551Z

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Observation bfa9de3f-ba96-4caa-ba05-51ddf548cc67 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:17.136720Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3e3539c5-1457-49e6-8a62-6b8cdde05f79 · outbound

This paper cites Peluse, Bounds for sets with no polynomial progressions, Forum Math.

Pointwise convergence of polynomial multiple ergodic averages along the primes Peluse, Bounds for sets with no polynomial progressions, Forum Math

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:16.923241Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b2d62234-160c-40b5-a8a8-08fa5e2b6f68 · outbound

This paper cites Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No.

Pointwise convergence of polynomial multiple ergodic averages along the primes Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:16.772622Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation baaf744a-bbca-4ad9-acf8-b3a092a80b63 · outbound

This paper cites Szemer´ edi.

Pointwise convergence of polynomial multiple ergodic averages along the primes Szemer´ edi

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:16.529503Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 73880ceb-f42b-4af5-9736-c2fdc541f97c · outbound

This paper cites Tao, Norm convergence of multiple ergodic averages for commuting transformations, Ergodic Theory Dynam.

Pointwise convergence of polynomial multiple ergodic averages along the primes Tao, Norm convergence of multiple ergodic averages for commuting transformations, Ergodic Theory Dynam

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:16.321552Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 73a6ae81-ac2a-434c-99c0-e55233e51190 · outbound

This paper cites Tao, The Ionescu-Wainger multiplier theorem and the adeles, Mathematika 67 (2021), 647-677.

Pointwise convergence of polynomial multiple ergodic averages along the primes Tao, The Ionescu-Wainger multiplier theorem and the adeles, Mathematika 67 (2021), 647-677

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:16.086287Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 236a01d4-f6c3-4953-90e2-a08f1c98b0e4 · outbound

This paper cites an unresolved cited work.

Pointwise convergence of polynomial multiple ergodic averages along the primes Unresolved cited work

Reference 52

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Observation dcb970ea-1c01-4d53-ac97-b652e418ce56 · outbound

This paper cites Pointwise convergence of ergodic averages with M\"obius weight.

Pointwise convergence of polynomial multiple ergodic averages along the primes Pointwise convergence of ergodic averages with M\"obius weight

Reference 53

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This paper cites Trojan, Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primes, Math.

Pointwise convergence of polynomial multiple ergodic averages along the primes Trojan, Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primes, Math

Reference 54

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This paper cites Walsh, Norm convergence of nilpotent ergodic averages, Ann.

Pointwise convergence of polynomial multiple ergodic averages along the primes Walsh, Norm convergence of nilpotent ergodic averages, Ann

Reference 55

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This paper cites Wierdl, Pointwise ergodic theorem along the prime numbers , Israel J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Wierdl, Pointwise ergodic theorem along the prime numbers , Israel J

Reference 56

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This paper cites Wooley, T.

Pointwise convergence of polynomial multiple ergodic averages along the primes Wooley, T

Reference 57

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This paper cites Ziegler, Universal characteristic factors and Furstenberg averages, J.

Pointwise convergence of polynomial multiple ergodic averages along the primes Ziegler, Universal characteristic factors and Furstenberg averages, J

Reference 58

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Pith citing papers

Observation b64aa57f-4366-4164-817b-8e026cea8c7b · inbound

Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials cites this paper.

Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials Pointwise convergence of polynomial multiple ergodic averages along the primes

Reference 67

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