Solutions of equations involving the modular j function

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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.

Original languageEnglish
Pages (from-to)3971-3998
Number of pages28
JournalTransactions of the American Mathematical Society
Volume374
Issue number6
DOIs
StatePublished - 2021
Externally publishedYes

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