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Paper Citation Record · LEDGER

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$

As of 12 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2509.04212.

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

pith.paper-citation-record.v1
2509.04212 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T10:30:45.676956Z

measured 38 of 38 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

38 of 38 outbound references displayed

  • verified exact8
  • verified fuzzy19
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b831d139-c4d8-449a-9819-821c23ef2c32 · outbound

This paper cites On $L^\alpha$-flatness of Erd\H{o}s-Littlewood's polynomials.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ On $L^\alpha$-flatness of Erd\H{o}s-Littlewood's polynomials

Reference 1

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local_arxiv, observed 2026-08-05T10:30:45.806034Z

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

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Observation c1f3b6ba-63b6-40d7-93a4-01b3732fe281 · outbound

This paper cites Some Notes on Flat Polynomials.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Some Notes on Flat Polynomials

Reference 2

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local_arxiv, observed 2026-08-05T10:30:45.792288Z

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Observation 527b4506-13da-445c-b2bc-14da04837bba · outbound

This paper cites On flat polynomials with non-Negative coefficients.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ On flat polynomials with non-Negative coefficients

Reference 3

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source=pdf_text observed=2026-08-05T10:30:45.548977Z digest=sha256:9ba5bc13e66dd24fb5621ab49bfb8292db04005b9dc83e0bfecabbdab2ed9781

Observation e0bf0108-78c6-4d1b-a3b7-6632785a2d7d · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 4

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

source=pdf_text observed=2026-08-05T10:30:45.552965Z digest=sha256:79c2696ec654e67f17a290aff12575f2224266290ab38c5baf4ce4d2b35c1e16

Observation 11460c9d-a431-42b8-a2e3-3032c3311795 · outbound

This paper cites Exponential sums of the M\"{o}bius function and flat polynomials.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Exponential sums of the M\"{o}bius function and flat polynomials

Reference 5

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local_arxiv, observed 2026-08-05T10:30:45.761839Z

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

source=pdf_text observed=2026-08-05T10:30:45.557050Z digest=sha256:703acd495044c74836e73474d25b517f906de2ce4668094da9bbe84c448a054f

Observation 23fb8963-25a7-49e3-a5a6-4019f8bc61f7 · outbound

This paper cites H., A Class of Littlewood Polynomials that are Not Lα-Flat ( with an appendix with M.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ H., A Class of Littlewood Polynomials that are Not Lα-Flat ( with an appendix with M

Reference 6

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

source=pdf_text observed=2026-08-05T10:30:45.561173Z digest=sha256:dddf0cd197d55cd0d6054b9ee101e3f70b7baebbf64c6e73d340edf269381915

Observation cbfd3b0e-a95a-4c6f-9052-19968f94bc29 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 7

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source=pdf_text observed=2026-08-05T10:30:45.565290Z digest=sha256:e19b00a88f97188e791e10967edb5505ecf22e4ee7e5bf969636e4beb25fe6cc

Observation db21194d-de35-4712-b0c3-470eac8f6847 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 8

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source=pdf_text observed=2026-08-05T10:30:45.568841Z digest=sha256:7958a21687b6f01e497f4bc2742d217eeee23dc1973ca3f72409428c62d2cab0

Observation e0f11f9e-6f99-43b1-b42d-5540ee66637f · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 9

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

source=pdf_text observed=2026-08-05T10:30:45.572895Z digest=sha256:b3101fda193ef099aaf04161d3f2e5f94ebf2d3a080de30174cea35a082fb432

Observation cfbe456e-baee-4984-adf7-93e0a1c20a6a · outbound

This paper cites Baker and G.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Baker and G

Reference 10

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source=pdf_text observed=2026-08-05T10:30:45.577096Z digest=sha256:2eea6bcafa525c79a03df00766d5c16638314d394fdc8f5e8b67b19e1e30a4b0

Observation 77143f17-c93b-4160-98b2-95a4327692ab · outbound

This paper cites Beller and D.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Beller and D

Reference 11

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source=pdf_text observed=2026-08-05T10:30:45.581116Z digest=sha256:10d52181d3eca5a7cfed09be2647118379403aaf762520bdc0f7bc9aa0873d03

Observation adc7def1-8c23-405a-834e-901db7e60277 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 12

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

source=pdf_text observed=2026-08-05T10:30:45.584584Z digest=sha256:4708c2dfb6c1a4d41b06e7b43f8f27176fa7026f23d537ee5cadf26f0a51464b

Observation 14a73602-216b-4deb-a980-259d493de896 · outbound

This paper cites Borwein and M.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Borwein and M

Reference 13

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source=pdf_text observed=2026-08-05T10:30:45.588349Z digest=sha256:bfb4177d2898462cb00f46deb93aebb80881984001e2aa7f29adc1b9897689c4

Observation ecc7ba5d-5258-441b-a13c-7f0f11d30a0f · outbound

This paper cites Borwein & M.J.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Borwein & M.J

Reference 14

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source=pdf_text observed=2026-08-05T10:30:45.592473Z digest=sha256:e4d6d0e8ac48ca2902b90075922089573ea5be3dd85261475b7eb2571f8a26ee

Observation 330e672c-df4d-444d-af8e-967aa3189b83 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 15

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

source=pdf_text observed=2026-08-05T10:30:45.596714Z digest=sha256:68579bf49fa04c11b264e6298ad2fa40028afd47fb4ea007dd60b971c3d7577f

Observation 9b514ba5-fa95-40d6-ae5c-d15a3b541409 · outbound

This paper cites The sequence of partial sums of a unimodular power series is not ultraflat.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ The sequence of partial sums of a unimodular power series is not ultraflat

Reference 16

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local_arxiv, observed 2026-08-05T10:30:45.747276Z

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

source=pdf_text observed=2026-08-05T10:30:45.600199Z digest=sha256:c3f4ada5b9161fbd83d26f8eca40a497c3fffd48cf4bb8766336bb431c883bf7

Observation 827c2998-d0f2-4a3e-a637-62c8c0893323 · outbound

This paper cites Erd˝ os, An inequality for the maximum of trigonometric, Ann.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Erd˝ os, An inequality for the maximum of trigonometric, Ann

Reference 17

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

source=pdf_text observed=2026-08-05T10:30:45.603974Z digest=sha256:512711180393cbeb941d8a6fe11a9e221a42e786a3622251004bcb3ec5d41389

Observation cd13355f-1199-477c-9392-0afdf70a14f8 · outbound

This paper cites Erd˝ os, Some unsolved problems, Michigan Math.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Erd˝ os, Some unsolved problems, Michigan Math

Reference 18

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source=pdf_text observed=2026-08-05T10:30:45.607903Z digest=sha256:03dbdcdcebe9864ba694007c051ae4809b18c782134da1238516d5edbf3d2647

Observation 0bb19193-5912-43f5-8851-d106dc926182 · outbound

This paper cites Erd˝ os, Problems and results on polynomials and interpolation.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Erd˝ os, Problems and results on polynomials and interpolation

Reference 19

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

source=pdf_text observed=2026-08-05T10:30:45.611644Z digest=sha256:201a9b9d28af414a6ef4de14a8928c9e9ccfe236b2c2d98548b3081016c0814e

Observation d5d59b6d-ab5d-46d6-851d-4f1649401409 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 20

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

source=pdf_text observed=2026-08-05T10:30:45.614845Z digest=sha256:e00e7045a83bb657b7739610dda985e0fd144386ed01141fed2a06a1ca44889f

Observation 258f6f18-718e-4403-83ab-daa42eae7ff8 · outbound

This paper cites Guenais, Morse cocycles and simple Lebesgue spectrum, Ergodic Theory Dynam.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Guenais, Morse cocycles and simple Lebesgue spectrum, Ergodic Theory Dynam

Reference 21

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source=pdf_text observed=2026-08-05T10:30:45.618131Z digest=sha256:2d48a3e66bffeca528b04dffa961c726a5b8b840919080a1fd2183a6a4b856f4

Observation 4907edea-98b0-4fda-8d73-12726d719eb4 · outbound

This paper cites Hajela and B.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Hajela and B

Reference 22

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source=pdf_text observed=2026-08-05T10:30:45.621202Z digest=sha256:3df5c9b4d3a0ea0431f062f703cd6d7ddd0ecd0d851e518f3af7f1df179e8a1a

Observation a2778326-80b0-48db-8da5-3a812814d116 · outbound

This paper cites Helson, Cocycles on the circle , J.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Helson, Cocycles on the circle , J

Reference 23

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source=pdf_text observed=2026-08-05T10:30:45.624583Z digest=sha256:eb5f6a7bb1f7e64421beb54ac1cedcb2ce634e0831a17b4c616b3e0cc217eab5

Observation 848ecebb-846a-463b-a6b9-bc90fbf487b1 · outbound

This paper cites Jedwab, A survey of the merit factor problem for binary sequences, In sequences and their applications-SETA 2004 (pp.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Jedwab, A survey of the merit factor problem for binary sequences, In sequences and their applications-SETA 2004 (pp

Reference 24

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

source=pdf_text observed=2026-08-05T10:30:45.627826Z digest=sha256:722cabadcb5fa860e856722ea7297d5bf4f2aa44f10420cb120a5bee9b6460ce

Observation 0988de4e-f0f4-4ce3-bfcb-aff0b9484d06 · outbound

This paper cites Kahane, Sur les polynˆ omes ` a coefficients unimodulaires,(French) Bull.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Kahane, Sur les polynˆ omes ` a coefficients unimodulaires,(French) Bull

Reference 25

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

source=pdf_text observed=2026-08-05T10:30:45.631269Z digest=sha256:e79de93fcc7406d13af99e62dd47276dd613105cde8cc87c3b149b242ca7ac32

Observation ac2418c1-69f4-432c-a14e-59e31b13e526 · outbound

This paper cites Koskela, Some generalizations of Clarkson’s inequalities,Publikacije Elek- trotehnickog Fakulteta.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Koskela, Some generalizations of Clarkson’s inequalities,Publikacije Elek- trotehnickog Fakulteta

Reference 26

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source=pdf_text observed=2026-08-05T10:30:45.634574Z digest=sha256:d46996ac82ae35175274abf68837211579bb978bad258bd68a1bbf239f0b54d3

Observation 75d83b0e-70dd-4fbb-a3a4-85ed7aaceac3 · outbound

This paper cites The London meetings 2012–2014.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ The London meetings 2012–2014

Reference 27

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

source=pdf_text observed=2026-08-05T10:30:45.638032Z digest=sha256:dad27dcc5e9aeaecc7aee59373b5eb6316fc1a2bead31ef3dd67f40ef8b35120

Observation c7166bb6-e9a9-4041-bab3-3ad4ec551853 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 28

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

source=pdf_text observed=2026-08-05T10:30:45.641419Z digest=sha256:b9252d1098d19adce28d2c456734292b7a51aa0b81f2d470e39742c97d56e726

Observation 3e20ba46-80f9-4356-8cd6-4de5d18cd6de · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 29

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raw_fallback, observed 2026-08-05T10:30:45.902211Z

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

source=pdf_text observed=2026-08-05T10:30:45.645644Z digest=sha256:e4e50509b03860ccb658afecdc64f9b44f9df8efaa9d8929ba9123af744ec744

Observation 91759b19-7e36-4e5f-b307-0db3e44fa90b · outbound

This paper cites Newman, Norms of polynomials, Amer.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Newman, Norms of polynomials, Amer

Reference 30

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raw_fallback, observed 2026-08-05T10:30:45.891507Z

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

source=pdf_text observed=2026-08-05T10:30:45.649031Z digest=sha256:dd2d84e182105704ee1e019ce10685c8000b1ad9b8852a634bc12f47b2c146b6

Observation 8c330d65-a3eb-4d4a-82fa-3efeaa15b6c4 · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 31

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raw_fallback, observed 2026-08-05T10:30:45.880380Z

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

source=pdf_text observed=2026-08-05T10:30:45.652392Z digest=sha256:fe08bb50749438ae9903b5481d44cd6f6ed311cacce0751cfc02da6c145a2934

Observation 0dd5b921-dbc9-47cb-a212-8e64e110139e · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 32

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raw_fallback, observed 2026-08-05T10:30:45.869941Z

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.

source=pdf_text observed=2026-08-05T10:30:45.656165Z digest=sha256:fb630e5b07dc2f87ddc5e1820513b4d85f2221e2460deda297a50478a9008b52

Observation 568bac35-b953-41e4-8b6b-6c4de2ca6e0c · outbound

This paper cites In: Butler S, Cooper J, Hurlbert G, eds.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ In: Butler S, Cooper J, Hurlbert G, eds

Reference 33

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

source=pdf_text observed=2026-08-05T10:30:45.659328Z digest=sha256:e79e2bb7e27a202bf3a1c7bef3fb681e78ea8ba766039b42131f4f9ab0d42dcf

Observation de387903-714b-470b-b904-501bbcfe66d5 · outbound

This paper cites Saffari, Barker sequences and Littlewood two-sided conjectures on polyno- mials with ±1 coefficients, S´ eminaire d’Analyse Harmonique, Ann´ ee 1989/90, 139–151, Univ.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Saffari, Barker sequences and Littlewood two-sided conjectures on polyno- mials with ±1 coefficients, S´ eminaire d’Analyse Harmonique, Ann´ ee 1989/90, 139–151, Univ

Reference 34

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raw_fallback, observed 2026-08-05T10:30:45.847859Z

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.

source=pdf_text observed=2026-08-05T10:30:45.663179Z digest=sha256:e6e00468248fb8e2ff020596e35a2a86c9860a4b28037266974121e6de89d533

Observation d31df6de-d86e-4792-adc4-8ae7175de5e8 · outbound

This paper cites Turyn and J.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Turyn and J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T10:30:45.836698Z

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.

source=pdf_text observed=2026-08-05T10:30:45.666332Z digest=sha256:99d49e7613991d2a972e90ebd249ae347362d8272a8b3a4d8813a6c51d3e4291

Observation 7428e7e6-d905-4b9e-b175-74a6add12b1c · outbound

This paper cites an unresolved cited work.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-05T10:30:45.826224Z

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.

source=pdf_text observed=2026-08-05T10:30:45.669910Z digest=sha256:8e561f80828760606426f394a7346eae5a1b7cec62b4329fdef2fcd5497ee185

Observation 6f988642-a77a-4093-b55e-3fe71913725a · outbound

This paper cites Yu, A Note on Barker Sequences and the L1-norm of Littlewood Poly- nomials, Comptes Rendus.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Yu, A Note on Barker Sequences and the L1-norm of Littlewood Poly- nomials, Comptes Rendus

Reference 37

Resolution
verified exact
doi, observed 2026-08-05T10:30:45.709040Z

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.

source=pdf_text observed=2026-08-05T10:30:45.673551Z digest=sha256:1786a748d497a4035dbfd6b09d15812c05ae08609ac4e56950f126a0ee96d7d3

Observation c62e6347-3192-4449-a732-d5a84428e3cb · outbound

This paper cites Zygmund, Trigonometric Series vol.

A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$ Zygmund, Trigonometric Series vol

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T10:30:45.816497Z

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.

source=pdf_text observed=2026-08-05T10:30:45.676956Z digest=sha256:17ad8a2aa87b69f31dae05889a43c588fb21474a319334406553ef8c49507133

Pith citing papers

No inbound Pith citation observations are available.