Birch & Swinnerton-Dyer conjecture

Importance: Outstanding ✭✭✭✭
Author(s):
Subject: Number Theory
Keywords:
Recomm. for undergrads: no
Prize: $1,000,000
Posted by: eyoong
on: May 12th, 2012

\begin{conjecture} Let $E/K$ be an elliptic curve over a number field $K$. Then the order of the zeros of its $L$-function, $L(E, s)$, at $s = 1$ is the Mordell-Weil rank of $E(K)$. \end{conjecture}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}

Bibliography

% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)


* indicates original appearance(s) of problem.