On singular moduli that are S-units

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  • Francesco Campagna
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.
Original languageEnglish
JournalManuscripta Mathematica
Volume166
Pages (from-to)73–90
ISSN0025-2611
DOIs
Publication statusPublished - 2021

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