2019/06/25 by Schmid, Stefan
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1906.10580
A result of Habegger shows that there are only finitely many singular moduli such that j or j-α is an algebraic unit. The result uses Duke's Equidistribution Theorem and is thus not effective. For a fixed j-invariant α∈ ℚ of an elliptic curve without complex multiplication, we prove that there are only finitely many singular moduli j such that j-α is an algebraic unit. The difference to the work of Habegger is that we give explicit bounds.