Eterović, S. orcid.org/0000-0001-6724-5887 (2025) Generic Solutions of Equations Involving the Modular j-function. Mathematische Annalen. ISSN 0025-5831
Abstract
Assuming a modular version of Schanuel’s conjecture and the modular Zilber–Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular j function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain versions of this result without relying on these conjectures, and even a result including the derivatives of j.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2024. 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/. |
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: | 08 Jan 2025 11:01 |
Last Modified: | 27 Jan 2025 15:43 |
Status: | Published online |
Publisher: | Springer |
Identification Number: | 10.1007/s00208-024-03082-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221418 |