The largest prime factor of n<SUP>2</SUP>+1and improvements on subexponential ABC

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dc.contributor.authorPasten, Hector
dc.date.accessioned2025-01-20T17:08:27Z
dc.date.available2025-01-20T17:08:27Z
dc.date.issued2024
dc.description.abstractWe combine transcendental methods and the modular approaches to the ABC conjecture to show that the largest prime factor of n(2)+1isatleastofsize(log(2)n)(2)/log(3)nwhere log k is the k-th iterate of the logarithm. This gives a substantial improvement on the best available estimates, which are essentially of size log2ngoing back to work of Chowla in 1934. Using the same ideas, we also obtain significant progress on sub expoential bounds for the ABC conjecture, which in a case gives the first improvement on a result by Stewart and Yu dating back over two decades. Central toour approach is the connection between Shimura curves and the ABC conjecture developed by the author.
dc.description.funderANID Fondecyt Regular from Chile
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00222-024-01244-6
dc.identifier.eissn1432-1297
dc.identifier.issn0020-9910
dc.identifier.urihttps://doi.org/10.1007/s00222-024-01244-6
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90951
dc.identifier.wosidWOS:001174066400001
dc.language.isoen
dc.revistaInventiones mathematicae
dc.rightsacceso restringido
dc.subject11J25
dc.subject11J86
dc.subject11G18
dc.titleThe largest prime factor of n<SUP>2</SUP>+1and improvements on subexponential ABC
dc.typeartículo
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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