http://openproblemgarden.org/op/birch_swinnerton_dyer_conjecture Comments for "Birch &amp; Swinnerton-Dyer conjecture" en http://openproblemgarden.org/op/birch_swinnerton_dyer_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/e312f209d206d253c41268eef2d6a484218ff003.png" alt="$ E/K $" /> be an elliptic curve over a number field <img class="teximage" src="/files/tex/fe461893b9f87593e8b79d83455b531cd9f29913.png" alt="$ K $" />. Then the order of the zeros of its <img class="teximage" src="/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png" alt="$ L $" />-function, <img class="teximage" src="/files/tex/2327f548d414998b97d9c91de7b744e595d7edf1.png" alt="$ L(E, s) $" />, at <img class="teximage" src="/files/tex/568a540383435c9518c0c52d3de199a0ef111f18.png" alt="$ s = 1 $" /> is the Mordell-Weil rank of <img class="teximage" src="/files/tex/964f2290addf5c893c353e20fc5a9ef1ac6840bd.png" alt="$ E(K) $" />. </div> </tr></td> </table> </td> </tr> </table> Number Theory http://openproblemgarden.org/op/birch_swinnerton_dyer_conjecture#comment Sat, 12 May 2012 00:48:07 +0200 eyoong 37423 at http://openproblemgarden.org