Differential existential closedness for the j-function

Vahagn Aslanyan; Sebastian Eterović; Jonathan Kirby

doi:10.1090/proc/15333

Differential existential closedness for the j-function

Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby

Logic

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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Abstract

We prove the Existential Closedness conjecture for the differential equation of the j-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j-function have solutions. Its consequences include a complete axiomatisation of 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.

Original language	English
Pages (from-to)	1417-1429
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	4
Early online date	13 Jan 2021
DOIs	https://doi.org/10.1090/proc/15333
Publication status	Published - Apr 2021

Keywords

Ax-Schanuel
j-function
Existential Closedness

Access to Document

10.1090/proc/15333

Accepted_ManuscriptAccepted author manuscript, 457 KB

Cite this

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Differential existential closedness for the j-function

Abstract

Keywords

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Jonathan Kirby

Exponentially Algebraically closed fields.

Cite this

Differential existential closedness for the j-function

Abstract

Keywords

Access to Document

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Jonathan Kirby

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Exponentially Algebraically closed fields.

Cite this