@Article{         10.2307/26395666,
  Author        = "Binyamini, Gal and Novikov, Dmitri",
  Abstract      = "We consider the structure ℝRE obtained from (ℝ, <, +, ·) by adjoining the restricted exponential and sine functions. We prove Wilkie's conjecture for sets definable in this structure: the number of rational points of height H in the transcendental part of any definable set is bounded by a polynomial in log H. We also prove two refined conjectures due to Pila concerning the density of algebraic points from a fixed number field, or with a fixed algebraic degree, for ℝRE-definable sets.",
  date-added    = "2023-04-06 08:20:20 +0200",
  date-modified = "2023-04-06 08:20:20 +0200",
  ISSN          = "0003486X",
  Journal       = "Annals of Mathematics",
  Number        = "1",
  Pages         = "237--275",
  Publisher     = "Annals of Mathematics",
  Title         = "Wilkie's conjecture for restricted elementary functions",
  URL           = "http://www.jstor.org/stable/26395666",
  URLDate       = "2023-04-06",
  Volume        = "186",
  Year          = "2017",
  bdsk-url-1    = "http://www.jstor.org/stable/26395666",
  File          = "Wilkie's conjecture for restricted elementary functions - 26395666 - a.pdf"
}

@Article{ 10.2307/26395666, Author = "Binyamini, Gal and Novikov, Dmitri", Abstract = "We consider the structure ℝRE obtained from (ℝ, <, +, ·) by adjoining the restricted exponential and sine functions. We prove Wilkie's conjecture for sets definable in this structure: the number of rational points of height H in the transcendental part of any definable set is bounded by a polynomial in log H. We also prove two refined conjectures due to Pila concerning the density of algebraic points from a fixed number field, or with a fixed algebraic degree, for ℝRE-definable sets.", date-added = "2023-04-06 08:20:20 +0200", date-modified = "2023-04-06 08:20:20 +0200", ISSN = "0003486X", Journal = "Annals of Mathematics", Number = "1", Pages = "237--275", Publisher = "Annals of Mathematics", Title = "Wilkie's conjecture for restricted elementary functions", URL = "http://www.jstor.org/stable/26395666", URLDate = "2023-04-06", Volume = "186", Year = "2017", bdsk-url-1 = "http://www.jstor.org/stable/26395666", File = "Wilkie's conjecture for restricted elementary functions - 26395666 - a.pdf" }