Solutions of equations involving the modular 𝑗 function

Eterović, Sebastian; Herrero, Sebastián

doi:10.1090/tran/8244

Solutions of equations involving the modular $j$ function
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by Sebastian Eterović and Sebastián Herrero PDF

Trans. Amer. Math. Soc. 374 (2021), 3971-3998 Request permission

Abstract:

Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular Schanuel conjecture implies that these systems have generic solutions. An unconditional result in this direction is proven for certain polynomial equations on $j$ with algebraic coefficients.

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