Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T11:58:37.743500Z
Paper Citation Record · LEDGER
Triple sums of Kloosterman sums and the discrepancy of modular inverses
As of 13 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 1 inbound Pith citation observation for arXiv:2411.17823.
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 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-21T23:19:48.196423Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T23:20:45.104250Z
Reference resolution
45 of 45 outbound references displayed
- verified exact1
- verified fuzzy29
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation d84d8f18-cd61-4cdd-82a6-57da49555df6 · outbound
This paper cites Andersson, ‘Summation formulae and zeta functions’, Ph.D.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Andersson, ‘Summation formulae and zeta functions’, Ph.D
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.591017Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cd3e9bb0-dbec-425a-9ba4-df0e75f059b0 · outbound
This paper cites Baier, ‘Multiplicative inverses in short intervals’, Int.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Baier, ‘Multiplicative inverses in short intervals’, Int
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.524965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9da269a6-f5ae-425f-ae19-4176aa451d43 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:39.509269Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 055802b4-f6fa-489f-bbe2-a7417db1a31d · outbound
This paper cites Bettin and V.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Bettin and V
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.491187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3ff7cd33-5b3d-4fbf-9a2d-244c89cd643a · outbound
This paper cites Blomer, J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Blomer, J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.475282Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 84750d71-0e0c-4097-b2f1-49fa65601456 · outbound
This paper cites Blomer and J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Blomer and J
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.314307Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3a31d63d-877d-40d4-a915-ce7bbeac0e4e · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:39.242023Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1a7b69d1-e27c-427b-9c60-9dea002e55ea · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:39.226290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 96d522f7-0279-4a2c-bdfa-26e25ec65e32 · outbound
This paper cites Deshouillers and H.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Deshouillers and H
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.210160Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 187de1b6-85fc-4dbe-8faa-76dd7ac1f976 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:39.194159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 34820e01-acfe-4fdf-a9eb-ebed5bcaf04d · outbound
This paper cites Dolgopyat, ‘On the distribution of the minimal solution of a linear Diophantine equation with random coefficients’, Funct.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Dolgopyat, ‘On the distribution of the minimal solution of a linear Diophantine equation with random coefficients’, Funct
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.178460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f5c103fd-df38-42ff-bbfa-6512d3b7b430 · outbound
This paper cites Drmota and R.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Drmota and R
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:39.117023Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8f3f82c0-007f-49c7-b297-7d1555ff3c1f · outbound
This paper cites Fujii, ‘On a problem of Dinaburg and Sinai’, Proc.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Fujii, ‘On a problem of Dinaburg and Sinai’, Proc
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.946494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e135555a-f8a0-45a8-9327-bb7abdd9f3a9 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.879003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 140bab82-ca78-446b-a13b-9b672e88fe34 · outbound
This paper cites Good, Local analysis of Selberg’s trace formula , Lecture Notes in Math., Vol.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Good, Local analysis of Selberg’s trace formula , Lecture Notes in Math., Vol
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.863885Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0609985f-f0c7-4dd8-95c8-11b4003c9200 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.847740Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 78b4a283-fffe-4aa5-9a50-ff0f5470484a · outbound
This paper cites Harcos and G.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Harcos and G
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.833202Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a3736a14-2237-4300-b44f-4a3813f313b3 · outbound
This paper cites Harman, ‘On the Erd˝ os–Tur´ an inequality for balls’,Acta Arith.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Harman, ‘On the Erd˝ os–Tur´ an inequality for balls’,Acta Arith
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.817846Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 17409d99-1a39-48ce-a9a2-82a178fd91e0 · outbound
This paper cites Humphries, ‘Distributing points on the torus via modular inverses’, Quart J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Humphries, ‘Distributing points on the torus via modular inverses’, Quart J
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.721056Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5deddb4f-f95c-4cd1-99e2-6ee81eff2600 · outbound
This paper cites Iwaniec and E.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Iwaniec and E
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.675400Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 91d3b355-9b84-4258-b76a-30b83c3f78ea · outbound
This paper cites Jutila, ‘On the spectral large sieve inequalities’, Funct.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Jutila, ‘On the spectral large sieve inequalities’, Funct
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.659713Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3af286fb-3e72-4284-880d-2b73f2cff3af · outbound
This paper cites Kerr, ‘Solutions to polynomial congruences in well shaped sets’, Bull.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Kerr, ‘Solutions to polynomial congruences in well shaped sets’, Bull
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.643929Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0af5be7f-b8a3-40e8-8158-3b6c56543545 · outbound
This paper cites Kerr and I.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Kerr and I
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.628672Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0998f38a-c44f-4b44-bd2a-71bbc4484b42 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.612089Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d78c8319-6dc5-42f3-b824-854aab10e831 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.532377Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a0f82d56-7281-4629-ac3c-8def027df6af · outbound
This paper cites Kuipers and H.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Kuipers and H
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.432079Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 89f230de-61fa-4b79-9e80-f7b7a33a9350 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.379786Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d2d87e5b-81ae-4229-98e6-373b6c403a97 · outbound
This paper cites Lam, ‘A local large sieve inequality for cusp forms’, J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Lam, ‘A local large sieve inequality for cusp forms’, J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.364303Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b38a8933-91b3-4ba5-8bb1-b06448c4c5f5 · outbound
This paper cites Lang, ‘A note on the measurability of convex sets’, Archiv Math.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Lang, ‘A note on the measurability of convex sets’, Archiv Math
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.349475Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2c62b536-ca62-42ec-a9b4-ad7b628a30c5 · outbound
This paper cites Liu, ’On Euler’s function’, Proc.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Liu, ’On Euler’s function’, Proc
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.334324Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2b13058c-db65-4336-96e5-e62541fd1a38 · outbound
This paper cites Philipp, ‘Empirical distribution functions and uniform distribution mod 1’, Diophantine Approx.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Philipp, ‘Empirical distribution functions and uniform distribution mod 1’, Diophantine Approx
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.318467Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 23078710-b309-4d92-a5cb-92c7e0495389 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.302336Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 07c6fb5f-616c-46c0-94f6-6a288c6a121b · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.286011Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d166c8ae-69a9-4908-a58f-a793dd7bcd65 · outbound
This paper cites Sarnak and J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Sarnak and J
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.270780Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 11f42a2f-76d5-4be5-8d50-d92841588098 · outbound
This paper cites Schmidt, ‘Irregularities of distribution.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Schmidt, ‘Irregularities of distribution
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.196494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b523a375-aaf1-495f-b0b9-35e0a7d8eafe · outbound
This paper cites Selberg, ‘ ¨Uber die Fourierkoeffizienten elliptischer Modulformen negativer Dimension’, C.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Selberg, ‘ ¨Uber die Fourierkoeffizienten elliptischer Modulformen negativer Dimension’, C
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.067759Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d1edef17-a512-4a98-a65b-99319b74446d · outbound
This paper cites Selberg, ‘Equidistribution in discrete groups and the spectral theory of automorphic forms’, 1977, available at http://Publications.IAS.Edu/Selberg/Section/2491.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Selberg, ‘Equidistribution in discrete groups and the spectral theory of automorphic forms’, 1977, available at http://Publications.IAS.Edu/Selberg/Section/2491
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:38.026043Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 63d30e93-cc9d-40f9-b2b8-db74cb9281fb · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:38.008609Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9dade219-d74f-4922-add4-f1c637648295 · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:37.992936Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f48b7f58-44db-4dd9-a96a-22560c74ed1a · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:37.975382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6d5e8038-9847-44ba-a0fb-1d2130329c5d · outbound
This paper cites Stefani, ‘On the monotonicity of perimeter of convex bodies’, J.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Stefani, ‘On the monotonicity of perimeter of convex bodies’, J
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:37.958545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 01e1491e-371a-4d45-9047-181d473dbe58 · outbound
This paper cites Sz¨ usz, ‘On a problem in the theory of uniform distribution’, Comptes Rendus Premier Congr` es Hongrois, Budapest, 1952, 461–472 (in Hungarian).
Triple sums of Kloosterman sums and the discrepancy of modular inverses Sz¨ usz, ‘On a problem in the theory of uniform distribution’, Comptes Rendus Premier Congr` es Hongrois, Budapest, 1952, 461–472 (in Hungarian)
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:37.942600Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fd7054ce-7725-4a92-93c7-01a97593fc9a · outbound
This paper cites an unresolved cited work.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T11:58:37.871014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c6483abd-1c90-470c-9879-f0c1cf0745de · outbound
This paper cites Walfisz, ‘Weylsche Exponentialsummen in der neueren Zahlentheorie’, Leipzig: B.G.
Triple sums of Kloosterman sums and the discrepancy of modular inverses Walfisz, ‘Weylsche Exponentialsummen in der neueren Zahlentheorie’, Leipzig: B.G
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T11:58:37.814611Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 74b9dce1-3cf6-449f-9529-413e7a1dca8c · outbound
This paper cites An elementary proof of the Selberg identity for Kloosterman sums.
Triple sums of Kloosterman sums and the discrepancy of modular inverses An elementary proof of the Selberg identity for Kloosterman sums
Reference 45
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T11:58:37.788059Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation a460b92c-5c8b-46ab-8e54-91106dbac5ed · inbound
On denominators of consecutive $\operatorname{SL}(2,{\mathbb N})$-saturated Farey fractions cites this paper.
On denominators of consecutive $\operatorname{SL}(2,{\mathbb N})$-saturated Farey fractions Triple sums of Kloosterman sums and the discrepancy of modular inverses
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-05-21T23:20:45.105918Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.