Generic Solutions of Equations Involving the Modular $j$-function

Abstract

Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain unconditional versions of this result.

40 pages, minor revisions

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Cited by in corpus (2)

• Some Equations Involving the Gamma Function
• Equations involving the modular $j$-function and its derivatives