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# Title: Weak Modular Zilber-Pink with Derivatives

Abstract: We formulate two weak versions of Pila's Modular Zilber-Pink with derivatives (MZPD) conjecture and prove them assuming a weak existential closedness conjecture for the differential equation of the $j$-function. Using those results we establish a weak Modular Andr\'{e}-Oort with derivatives statement unconditionally. Then using Andr\'{e}-Oort we give an unconditional proof for a special case of one of the aforementioned weak MZPD conjectures.
 Comments: 29 pages Subjects: Number Theory (math.NT); Logic (math.LO) Cite as: arXiv:1803.05895 [math.NT] (or arXiv:1803.05895v1 [math.NT] for this version)

## Submission history

From: Vahagn Aslanyan [view email]
[v1] Thu, 15 Mar 2018 17:49:32 GMT (40kb)