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Article: Equidistribution of Heegner points and ternary quadratic forms

TitleEquidistribution of Heegner points and ternary quadratic forms
Authors
Keywords11G05
11E20
11E45
Issue Date2011
Citation
Mathematische Annalen, 2011, v. 350 n. 3, p. 501-532 How to Cite?
AbstractWe prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize an equidistribution result with respect to a single reduction map established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system.
Persistent Identifierhttp://hdl.handle.net/10722/192196
ISSN
2015 Impact Factor: 1.366
2015 SCImago Journal Rankings: 3.112
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorJetchev, Den_US
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:18Z-
dc.date.available2013-10-23T09:27:18Z-
dc.date.issued2011en_US
dc.identifier.citationMathematische Annalen, 2011, v. 350 n. 3, p. 501-532en_US
dc.identifier.issn0025-5831en_US
dc.identifier.urihttp://hdl.handle.net/10722/192196-
dc.description.abstractWe prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize an equidistribution result with respect to a single reduction map established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system.-
dc.languageengen_US
dc.relation.ispartofMathematische Annalenen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject11G05-
dc.subject11E20-
dc.subject11E45-
dc.titleEquidistribution of Heegner points and ternary quadratic formsen_US
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.1007/s00208-010-0568-5en_US
dc.identifier.scopuseid_2-s2.0-79958231701en_US
dc.identifier.volume350en_US
dc.identifier.issue3en_US
dc.identifier.spage501en_US
dc.identifier.epage532en_US
dc.identifier.isiWOS:000291485800001-

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