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arXiv · 2102.06396

Effective bounds on differences of singular moduli that are S-units

Francesco Campagna
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Abstract

Given a singular modulus $j_0$ and a set of rational primes $S$, we study the problem of effectively determining the set of singular moduli $j$ such that $j-j_0$ is an $S$-unit. For every $j_0 \neq 0$, we provide an effective way of finding this set for infinitely many choices of $S$. The same is true if $j_0=0$ 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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Francesco Campagna. 2022-10-03. Effective bounds on differences of singular moduli that are S-units. https://doi.org/10.1017/s0305004122000378

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