On singular moduli that are S-units [article]

Francesco Campagna
2019 arXiv   pre-print
Recently Yu. Bilu, P. Habegger and L. K\"uhne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units. Here we prove that when the set S contains only primes congruent to 1 modulo 3 then no singular modulus can be an S-unit. We then give some remarks on the general case and we study the norm factorizations of a special family of singular moduli.
arXiv:1904.08958v1 fatcat:4npocxowh5dgfavt76ybvuecse