  We give an integral representation for solutions to the quantized Knizhnik-
Zamolodchikov equation (qKZ) associated with the Lie algebra $gl_{N+1}$.
Asymptotic solutions to qKZ are constructed. The leading term of an asymptotic
solution is the Bethe vector -- an eigenvector of the transfer-matrix of a
quantum spin chain model. We show that the norm of the Bethe vector is equal to
the product of the Hessian of a suitable function and an explicitly written
rational function. This formula is a generalization of the Gaudin-Korepin
formula for a norm of the Bethe vector. We show that, generically, the Bethe
vectors form a base for the $gl_2$ case.
