Aslanyan, V, Eterovic, S orcid.org/0000-0001-6724-5887 and Kirby, J (2021) Differential existential closedness for the j-function. Proceedings of the American Mathematical Society, 149 (4). pp. 1417-1429. ISSN 0002-9939
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Copyright 2021 American Mathematical Society. This is an author produced version of an article, published in Proceedings of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Ax-Schanuel; Existential Closedness; j-function |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Nov 2022 15:18 |
Last Modified: | 03 Nov 2022 15:26 |
Status: | Published |
Publisher: | American Mathematical Society |
Identification Number: | 10.1090/proc/15333 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:192774 |