On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication
Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family of quadratic twists. In particular, we prove a lower bound for this valuation in terms of the Tamagawa number in a form...
| Auteurs principaux: | , , , |
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| Format: | Journal article |
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Mathematical Institutes of the Universität Münster
2013
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| _version_ | 1826275511086612480 |
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| author | Coates, J Kim, M Liang, Z Zhao, C |
| author_facet | Coates, J Kim, M Liang, Z Zhao, C |
| author_sort | Coates, J |
| collection | OXFORD |
| description | Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family of quadratic twists. In particular, we prove a lower bound for this valuation in terms of the Tamagawa number in a form predicted by the conjecture of Birch and Swinnerton-Dyer. |
| first_indexed | 2024-03-06T22:59:49Z |
| format | Journal article |
| id | oxford-uuid:61b5d3aa-dc69-4eb6-8bce-591851e1561a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:59:49Z |
| publishDate | 2013 |
| publisher | Mathematical Institutes of the Universität Münster |
| record_format | dspace |
| spelling | oxford-uuid:61b5d3aa-dc69-4eb6-8bce-591851e1561a2022-03-26T18:01:40ZOn the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplicationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:61b5d3aa-dc69-4eb6-8bce-591851e1561aSymplectic Elements at OxfordMathematical Institutes of the Universität Münster2013Coates, JKim, MLiang, ZZhao, CGiven an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family of quadratic twists. In particular, we prove a lower bound for this valuation in terms of the Tamagawa number in a form predicted by the conjecture of Birch and Swinnerton-Dyer. |
| spellingShingle | Coates, J Kim, M Liang, Z Zhao, C On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication |
| title | On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic
curves with complex multiplication |
| title_full | On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic
curves with complex multiplication |
| title_fullStr | On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic
curves with complex multiplication |
| title_full_unstemmed | On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic
curves with complex multiplication |
| title_short | On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic
curves with complex multiplication |
| title_sort | on the 2 part of the birch swinnerton dyer conjecture for elliptic curves with complex multiplication |
| work_keys_str_mv | AT coatesj onthe2partofthebirchswinnertondyerconjectureforellipticcurveswithcomplexmultiplication AT kimm onthe2partofthebirchswinnertondyerconjectureforellipticcurveswithcomplexmultiplication AT liangz onthe2partofthebirchswinnertondyerconjectureforellipticcurveswithcomplexmultiplication AT zhaoc onthe2partofthebirchswinnertondyerconjectureforellipticcurveswithcomplexmultiplication |