On singular moduli that are S-units
Number Theory
2020-08-26 v2 Algebraic Geometry
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.
Cite
@article{arxiv.1904.08958,
title = {On singular moduli that are S-units},
author = {Francesco Campagna},
journal= {arXiv preprint arXiv:1904.08958},
year = {2020}
}
Comments
Version changed according to the referee's comments. The final version appears in Manuscripta Mathematica, https://doi.org/10.1007/s00229-020-01230-1