Projects per year
Abstract
We prove the Existential Closedness conjecture for the differential equation of the jfunction and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the jfunction have solutions. Its consequences include a complete axiomatisation of jreducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular ZilberPink with Derivatives conjecture.
Original language  English 

Pages (fromto)  14171429 
Number of pages  13 
Journal  Proceedings of the American Mathematical Society 
Volume  149 
Issue number  4 
Early online date  13 Jan 2021 
DOIs  
Publication status  Published  Apr 2021 
Keywords
 AxSchanuel
 jfunction
 Existential Closedness
Profiles

Jonathan Kirby
 School of Mathematics  Reader
 Logic  Member
Person: Research Group Member, Academic, Teaching & Research
Projects
 1 Finished

Exponentially Algebraically closed fields.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research