Factors of polynomials computed by small constant-depth circuits or formulas are themselves computable by small constant-depth circuits or formulas in characteristic zero and large positive characteristic.
Explicit Implicit Function Theorem for All Fields
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abstract
We give an explicit implicit function theorem for formal power series that is valid for all fields, which implies in particular Lagrange inversion formula and and Flajolet-Soria coefficient extraction formula known for fields of characteristic 0.
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Closure under factorization from a result of Furstenberg
Factors of polynomials computed by small constant-depth circuits or formulas are themselves computable by small constant-depth circuits or formulas in characteristic zero and large positive characteristic.