On singular moduli that are S-units
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On singular moduli that are S-units. / Campagna, Francesco.
I: Manuscripta Mathematica, Bind 166, 2021, s. 73–90.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On singular moduli that are S-units
AU - Campagna, Francesco
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
U2 - 10.1007/s00229-020-01230-1
DO - 10.1007/s00229-020-01230-1
M3 - Journal article
VL - 166
SP - 73
EP - 90
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
ER -
ID: 257327688