There are at most finitely many singular moduli that are S-units
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...
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| creator | Herrero, Sebastián Menares, Ricardo Rivera-Letelier, Juan |
| description | 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 to 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. |
| doi_str_mv | 10.48550/arxiv.2102.05041 |
| format | Article |
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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 to 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.</description><identifier>DOI: 10.48550/arxiv.2102.05041</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Dynamical Systems ; Mathematics - Number Theory</subject><creationdate>2021-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2102.05041$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2102.05041$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Herrero, Sebastián</creatorcontrib><creatorcontrib>Menares, Ricardo</creatorcontrib><creatorcontrib>Rivera-Letelier, Juan</creatorcontrib><title>There are at most finitely many singular moduli that are S-units</title><description>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 to 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
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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 to 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.</abstract><doi>10.48550/arxiv.2102.05041</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Dynamical Systems Mathematics - Number Theory |
| title | There are at most finitely many singular moduli that are S-units |
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