Editing L-function (section)

== Birch and Swinnerton-Dyer conjecture ==
{{main|Birch and Swinnerton-Dyer conjecture}}

One of the influential examples, both for the history of the more general ''L''-functions and as a still-open research problem, is the conjecture developed by [[Bryan Birch]] and [[Peter Swinnerton-Dyer]] in the early part of the 1960s. It applies to an [[elliptic curve]] ''E'', and the problem it attempts to solve is the prediction of the rank of the elliptic curve over the rational numbers (or another [[global field]]): i.e. the number of free generators of its group of rational points. Much previous work in the area began to be unified around a better knowledge of ''L''-functions. This was something like a paradigm example of the nascent theory of ''L''-functions.