Differential Existential Closedness for the j-function

Aslanyan, Vahagn, Eterović, Sebastian and Kirby, Jonathan (2020) Differential Existential Closedness for the j-function. Proceedings of the American Mathematical Society. ISSN 0002-9939 (In Press)

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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.

Item Type: Article
Uncontrolled Keywords: ax-schanuel,j-function,existential closedness
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: LivePure Connector
Date Deposited: 14 Sep 2020 23:52
Last Modified: 16 Sep 2020 23:57
URI: https://ueaeprints.uea.ac.uk/id/eprint/76873
DOI:

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