A Diophantine approach to the three and four exponentials conjectures

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Some special cases of Wilkie's conjecture are shown to be equivalent to real versions of the three and four exponentials conjectures. Wilkie's conjecture is an open problem originating in model theory that concerns the density of algebraic points in sets defined using the exponential function; the latter conjectures concern the algebraic nature of values of the exponential function.
Original languageEnglish
Pages (from-to)199-221
Number of pages23
JournalRamanujan Journal
Issue number1
Early online date13 Oct 2015
Publication statusPublished - 1 Jan 2017


  • transcendence
  • exponential function
  • logarithms of algebraic numbers
  • algebraic independence


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