Differential existential closedness for the 𝑗-function-Reference-Cited by-同舟云学术

Differential existential closedness for the 𝑗-function

Published:2021-01-13 Issue:4 Volume:149 Page:1417-1429
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Aslanyan Vahagn,Eterović Sebastian,Kirby Jonathan

Abstract

We prove the Existential Closedness conjecture for the differential equation of the j j -function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j j -function have solutions. Its consequences include a complete axiomatisation of j j -reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.

Funder

Engineering and Physical Sciences Research Council

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2021-149-04/S0002-9939-2021-15333-1/proc15333_AM.pdf

Reference19 articles.

1. [Asl18a] Vahagn Aslanyan, Adequate predimension inequalities in differential fields, Preprint, arXiv:1803.04753, 2018.

2. [Asl18b] Vahagn Aslanyan, Weak Modular Zilber-Pink with Derivatives, Preprint, arXiv:1803.05895, 2018.

3. Ax-Schanuel and strong minimality for the 𝑗-function;Aslanyan, Vahagn;Ann. Pure Appl. Logic,2021

4. On Schanuel’s conjectures;Ax, James;Ann. of Math. (2),1971

5. Pseudo-exponential maps, variants, and quasiminimality;Bays, Martin;Algebra Number Theory,2018

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A closure operator respecting the modular j-function;Israel Journal of Mathematics;2022-10-05

2. Adequate predimension inequalities in differential fields;Annals of Pure and Applied Logic;2022-01

3. Blurrings Of The J-Function;The Quarterly Journal of Mathematics;2021-08-14

4. Weak modular Zilber–Pink with derivatives;Mathematische Annalen;2021-05-24