Effective bounds on differences of singular moduli that are S-units
Abstract
Given a singular modulus j0 and a set of rational primes S, we study the problem of effectively determining the set of singular moduli j such that j-j0 is an S-unit. For every j0 ≠ 0, we provide an effective way of finding this set for infinitely many choices of S. The same is true if j0=0 and we assume the Generalized Riemann Hypothesis. Certain numerical experiments will also lead to the formulation of a "uniformity conjecture" for singular S-units.
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