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Mathematics > Classical Analysis and ODEs

arXiv:1805.10551 (math)
[Submitted on 26 May 2018 (v1), last revised 24 Aug 2020 (this version, v3)]

Title:An $l^2$ decoupling interpretation of efficient congruencing: the parabola

Authors:Zane Kun Li
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Abstract:We give a new proof of $l^2$ decoupling for the parabola inspired from efficient congruencing. Making quantitative this proof matches a bound obtained by Bourgain for the discrete restriction problem for the parabola. We illustrate similarities and differences between this new proof and efficient congruencing and the proof of decoupling by Bourgain and Demeter. We also show where tools from decoupling such as $l^2 L^2$ decoupling, Bernstein, and ball inflation come into play.
Comments: 36 pages; revised version incorporating referee comments
Subjects: Classical Analysis and ODEs (math.CA); Number Theory (math.NT)
Cite as: arXiv:1805.10551 [math.CA]
  (or arXiv:1805.10551v3 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.1805.10551

Submission history

From: Zane Li [view email]
[v1] Sat, 26 May 2018 23:05:29 UTC (22 KB)
[v2] Thu, 25 Jul 2019 20:55:18 UTC (21 KB)
[v3] Mon, 24 Aug 2020 22:59:23 UTC (29 KB)
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