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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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
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?...
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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