Broudy, IA and Eterovic, S orcid.org/0000-0001-6724-5887 (2023) Schanuel Type Conjectures and Disjointness. The Ramanujan Journal, 62. pp. 781-795. ISSN 1382-4090
Abstract
Given a subfield F of C, we study the linear disjointess of the field E generated by iterated exponentials of elements of F̅, and the field L generated by iterated logarithms, in the presence of Schanuel’s conjecture. We also obtain similar results replacing exp by the modular j-function, under an appropriate version of Schanuel’s conjecture, where linear disjointness is replaced by a notion coming from the action of GL₂ on C. We also show that for certain choices of F we obtain unconditional versions of these statements.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Complex exponential; j-Function; Linear disjointness; G-disjointness; Schanuel’s conjecture; Ax–Schanuel |
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: | 20 Feb 2023 16:35 |
Last Modified: | 26 Oct 2023 12:03 |
Published Version: | https://link.springer.com/article/10.1007/s11139-0... |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11139-023-00707-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:196440 |