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On singular moduli that are S-units

Published 18 Apr 2019 in math.NT and math.AG | (1904.08958v2)

Abstract: 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.

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Authors (1)

  1. Francesco Campagna 

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