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Aslanyan, Vahagn and Kirby, Jonathan 
ORCID: https://orcid.org/0000-0003-4031-9107
(2022)
Blurrings of the j-function.
The Quarterly Journal of Mathematics, 73 (2).
461–475.
ISSN 0033-5606
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Abstract
Inspired by the idea of blurring the exponential function, we define blurred variants of the j-function and its derivatives, where blurring is given by the action of a subgroup of (GL)2 (C). For a dense subgroup (in the complex topology) we prove an Existential Closedness theorem which states that all systems of equations in terms of the corresponding blurred j with derivatives have complex solutions, except where there is a functional transcendence reason why they should not. For the j-function without derivatives we prove a stronger theorem, namely, Existential Closedness for j blurred by the action of a subgroup which is dense in (GL)2+ (ℝ;)), but not necessarily in (GL)2 (C))). We also show that for a suitably chosen countable algebraically closed subfield C (C)), the complex field augmented with a predicate for the blurring of the j-function by (GL)2 (C) is model theoretically tame, in particular, ω-stable and quasiminimal.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600 |
| Faculty \ School: | Faculty of Science > School of Mathematics |
| UEA Research Groups: | Faculty of Science > Research Groups > Logic |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 27 Nov 2021 01:48 |
| Last Modified: | 21 Apr 2023 01:16 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/82385 |
| DOI: | 10.1093/qmath/haab037 |
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