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Birch and swinnerton dyer conjecture

Birch and Swinnerton Dyer conjecture

This conjecture is one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute. This problem purely depends on number theory and is widely recognized as most challenging problem. This conjecture relates the arithmetic data associated to an elliptic curve E over a number field K to the behavior of the Hasse Weil L-function, ie L(E, s) of E at s = 1. So far this conjecture problem has not been proved and only special cases of the conjecture have been proved.

The problem was named after Peter Swinnerton and Dyer who in 1960's used computer at University of Cambridge Computer Laboratory developed the conjecture when trying to calculate the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known.

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