Joint distribution for the Selmer ranks of the congruent number curves.
| Autor: | Vrećica, Ilija S. |
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| Jazyk: | angličtina |
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| Druh dokumentu: | Non-fiction |
| ISSN: | 0011-4642 |
| Abstrakt: | Abstract: We determine the distribution over square-free integers $n$ of the pair $(\dim_{\mathbb{F}_2}{\rm Sel}^\Phi(E_n/\mathbb{Q}),\dim_{\mathbb{F}_2} {\rm Sel}^{\widehat{\Phi}}(E_n'/\mathbb{Q}))$, where $E_n$ is a curve in the congruent number curve family, $E_n'\colon y^2=x^3+4n^2x$ is the image of isogeny $\Phi\colon E_n\rightarrow E_n'$, $\Phi(x,y)=(y^2/x^2,y(n^2-x^2)/x^2)$, and $\widehat{\Phi}$ is the isogeny dual to $\Phi$. |
| Databáze: | Katalog Knihovny AV ČR |
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