Blurrings of the j-function

Aslanyan, Vahagn and Kirby, Jonathan (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
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 27 Nov 2021 01:48
Last Modified: 22 Oct 2022 16:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/82385
DOI: 10.1093/qmath/haab037

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