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Mathematics > Logic

arXiv:1804.08232 (math)
[Submitted on 23 Apr 2018 (v1), last revised 27 Feb 2019 (this version, v2)]

Title:Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces

Authors:Gareth O. Jones, Margaret E. M. Thomas
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Abstract:We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaffian functions. The class of surfaces to which our result applies includes, for instance, graphs of unrestricted Pfaffian functions defined on the plane.
Comments: 32 pages
Subjects: Logic (math.LO); Number Theory (math.NT)
MSC classes: 03C64 (Primary) 14G05, 14Q20 (Secondary)
Cite as: arXiv:1804.08232 [math.LO]
  (or arXiv:1804.08232v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1804.08232

Submission history

From: Margaret E. M. Thomas [view email]
[v1] Mon, 23 Apr 2018 02:51:52 UTC (35 KB)
[v2] Wed, 27 Feb 2019 20:57:44 UTC (35 KB)
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