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Article: Equidistribution of Heegner points and ternary quadratic forms
Title | Equidistribution of Heegner points and ternary quadratic forms |
---|---|
Authors | |
Keywords | 11G05 11E20 11E45 |
Issue Date | 2011 |
Citation | Mathematische Annalen, 2011, v. 350 n. 3, p. 501-532 How to Cite? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/192196 |
ISSN | 2021 Impact Factor: 1.334 2020 SCImago Journal Rankings: 2.235 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Jetchev, D | en_US |
dc.contributor.author | Kane, B | en_US |
dc.date.accessioned | 2013-10-23T09:27:18Z | - |
dc.date.available | 2013-10-23T09:27:18Z | - |
dc.date.issued | 2011 | en_US |
dc.identifier.citation | Mathematische Annalen, 2011, v. 350 n. 3, p. 501-532 | en_US |
dc.identifier.issn | 0025-5831 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/192196 | - |
dc.description.abstract | We 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.language | eng | en_US |
dc.relation.ispartof | Mathematische Annalen | en_US |
dc.subject | 11G05 | - |
dc.subject | 11E20 | - |
dc.subject | 11E45 | - |
dc.title | Equidistribution of Heegner points and ternary quadratic forms | en_US |
dc.type | Article | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1007/s00208-010-0568-5 | en_US |
dc.identifier.scopus | eid_2-s2.0-79958231701 | en_US |
dc.identifier.volume | 350 | en_US |
dc.identifier.issue | 3 | en_US |
dc.identifier.spage | 501 | en_US |
dc.identifier.epage | 532 | en_US |
dc.identifier.isi | WOS:000291485800001 | - |
dc.identifier.issnl | 0025-5831 | - |