Blurrings of the j-function

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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	27 Nov 2021 01:48
Last Modified:	07 Nov 2024 12:44
URI:	https://ueaeprints.uea.ac.uk/id/eprint/82385
DOI:	10.1093/qmath/haab037

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