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- Title
There are at most finitely many singular moduli that are S -units.
- Authors
Herrero, Sebastián; Menares, Ricardo; Rivera-Letelier, Juan
- Abstract
We show that for every finite set of prime numbers $S$ , there are at most finitely many singular moduli that are $S$ -units. The key new ingredient is that for every prime number $p$ , singular moduli are $p$ -adically disperse. We prove analogous results for the Weber modular functions, the $\lambda$ -invariants and the McKay–Thompson series associated with the elements of the monster group. Finally, we also obtain that a modular function that specializes to infinitely many algebraic units at quadratic imaginary numbers must be a weak modular unit.
- Subjects
MODULAR functions; PRIME numbers; WEBER functions; MODULAR groups
- Publication
Compositio Mathematica, 2024, Vol 160, Issue 4, p732
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X23007704