Differential existential closedness for the j-function

Aslanyan, Vahagn, Eterović, Sebastian and Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107 (2021) Differential existential closedness for the j-function. Proceedings of the American Mathematical Society, 149 (4). pp. 1417-1429. ISSN 0002-9939

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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.

Item Type: Article
Uncontrolled Keywords: ax-schanuel,j-function,existential closedness
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
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Depositing User: LivePure Connector
Date Deposited: 14 Sep 2020 23:52
Last Modified: 21 Apr 2023 00:46
URI: https://ueaeprints.uea.ac.uk/id/eprint/76873
DOI: 10.1090/proc/15333


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