Unsolved Problems

Extend the Kronecker-Weber theorem on abelian extensions of the rationals to any base number field....

If $\alpha$ is algebraic and irrational, and $\beta$ is algebraic and irrational, is $\alpha^\beta$ transcendental?...

Generalize the reciprocity law of number theory to arbitrary number fields....

Extend the theory of quadratic forms with algebraic numerical coefficients....