Differential existential closedness for the j-function

Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby

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We prove the Existential Closedness conjecture for the differential equation of the j-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j-function have solutions. Its consequences include a complete axiomatisation of j-reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.
Original languageEnglish
Pages (from-to)1417-1429
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number4
Early online date13 Jan 2021
Publication statusPublished - Apr 2021


  • Ax-Schanuel
  • j-function
  • Existential Closedness

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