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- W4300007241 abstract "Let $A/mathbb{Q}$ be an elliptic curve having split multiplicative reduction at an odd prime $p$. Under some mild technical assumptions, we prove the statement: $$rank_{mathbb{Z}}A(mathbb{Q})=1 and #Big(underline{III}(A/mathbb{Q})[p^infty]Big)<infty implies mathrm{ord}_{s=1}L(A/mathbb{Q},s)=1,$$ thus providing a $p$-converse to a celebrated theorem of Kolyvagin-Gross-Zagier." @default.
- W4300007241 created "2022-10-03" @default.
- W4300007241 creator A5021001737 @default.
- W4300007241 date "2014-07-07" @default.
- W4300007241 modified "2023-09-28" @default.
- W4300007241 title "On the p-converse of the Kolyvagin-Gross-Zagier theorem" @default.
- W4300007241 doi "https://doi.org/10.48550/arxiv.1407.1816" @default.
- W4300007241 hasPublicationYear "2014" @default.
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