HomePublications

Differential Existential Closedness for the j-function

Research output: Contribution to journalArticle

Open Access permissions

Open

Documents

Authors

Organisational units

Abstract

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.

Details

Original languageEnglish
JournalProceedings of the American Mathematical Society
Publication statusAccepted/In press - 4 Sep 2020
Peer-reviewedYes

Keywords

    Research areas

  • Ax-Schanuel, j-function, Existential Closedness

View graph of relations

ID: 184237532

Related by author
  1. Ax-Schanuel and strong minimality for the j-function

    Research output: Contribution to journalArticle

  2. Existentially closed De Morgan algebras

    Research output: Contribution to journalArticle

  3. Blurred Complex Exponentiation

    Research output: Contribution to journalArticle

  4. On local definability of holomorphic functions

    Research output: Contribution to journalArticle

  5. Existentially closed exponential fields

    Research output: Contribution to journalArticle

Related by journal
  1. The Morris model

    Research output: Contribution to journalArticle

  2. Time-changes preserving zeta functions

    Research output: Contribution to journalArticle

  3. Mertens' theorem for toral automorphisms

    Research output: Contribution to journalArticle

  4. Orbit-counting for nilpotent group shifts

    Research output: Contribution to journalArticle