Vahagn Aslanyan
Published 2018-03-15Version 1
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.
On derivatives of zeta and $L$-functions near the 1-line
Derivatives of Frobenius and Derivatives of Hodge weights
Derivatives of L-functions
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