The Birch–Tate conjecture is based on algebraic K-theory proposed by both Bryan John Birch and John Tate. It relates the value of a Dedekind zeta function at s = −1 to the order of K2 of the ring of integers, for a number field F.
Progress on this conjecture has been made as a consequence of work on Iwasawa theory, and in particular of the proofs given for the so-called "main conjecture of Iwasawa theory."
The problem remains unsolved as of 2011.