  We consider the asymptotic behavior of the second mixed moment of the
characteristic polynomials of the 1D Gaussian band matrices, i.e. of the
hermitian matrices $H_n$ with independent Gaussian entries such that $<
H_{ij}H_{lk}>=\delta_{ik}\delta_{jl}J_{ij}$, where $J=(-W^2\triangle+1)^{-1}$.
Assuming that $W^2=n^{1+\theta}$, $0<\theta<1$, we show that this asymptotic
behavior (as $n\to\infty$) in the bulk of the spectrum coincides with those for
the Gaussian Unitary Ensemble.
