  The problem of anomalous scaling in magnetohydrodynamics turbulence is
considered within the framework of the kinematic approximation, in the presence
of a large-scale background magnetic field. The velocity field is Gaussian,
$\delta$-correlated in time, and scales with a positive exponent $\xi$.
Explicit inertial-range expressions for the magnetic correlation functions are
obtained; they are represented by superpositions of power laws with
non-universal amplitudes and universal (independent of the anisotropy and
forcing) anomalous exponents. The complete set of anomalous exponents for the
pair correlation function is found non-perturbatively, in any space dimension
$d$, using the zero-mode technique. For higher-order correlation functions, the
anomalous exponents are calculated to $O(\xi)$ using the renormalization group.
The exponents exhibit a hierarchy related to the degree of anisotropy; the
leading contributions to the even correlation functions are given by the
exponents from the isotropic shell, in agreement with the idea of restored
small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in
the odd correlation functions : the skewness factor is slowly decreasing going
down to small scales and higher odd dimensionless ratios (hyperskewness etc.)
dramatically increase, thus diverging in the $r\to 0$ limit.
