Shimura curves and the abc conjecture

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dc.contributor.authorPasten, Hector
dc.date.accessioned2025-01-20T17:11:43Z
dc.date.available2025-01-20T17:11:43Z
dc.date.issued2024
dc.description.abstractIn this work we develop a framework that enables the use of Shimura curve parametrizations of elliptic curves to approach the abc conjecture, leading to a number of new unconditional applications over Q and, more generally, totally real number fields. Several results of independent interest are obtained along the way, such as bounds for the Manin constant, a study of the congruence number, extensions of the Ribet-Takahashi formula, and lower bounds for the L2-norm of integral quaternionic modular forms.The methods require a number of tools from Arakelov geometry, analytic number theory, Galois representations, complex-analytic estimates on Shimura curves, automorphic forms, known cases of the Colmez conjecture, and results on generalized Fermat equations.& COPY; 2023 Published by Elsevier Inc.
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.jnt.2023.07.002
dc.identifier.eissn1096-1658
dc.identifier.issn0022-314X
dc.identifier.urihttps://doi.org/10.1016/j.jnt.2023.07.002
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91203
dc.identifier.wosidWOS:001073082200001
dc.language.isoen
dc.pagina.final335
dc.pagina.inicio214
dc.revistaJournal of number theory
dc.rightsacceso restringido
dc.subjectShimura curves
dc.subjectElliptic curves
dc.subjectabc conjecture
dc.titleShimura curves and the abc conjecture
dc.typeartículo
dc.volumen254
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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