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arXiv · 2003.10996

Differential Existential Closedness for the $j$-function

Vahagn Aslanyan·Sebastian Eterović·Jonathan Kirby
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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.

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BibTeXRIS

Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby. 2020-03-24. Differential Existential Closedness for the $j$-function. https://doi.org/10.1090/proc/15333

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