  In this paper we present the 1-loop perturbative computation of the
renormalization constants and mixing coefficients of the lattice quark
operators of rank three whose hadronic elements enter in the determination of
the second moment of Deep Inelastic Scattering (DIS) structure functions.
  We have employed in our calculations the nearest-neighbor improved
``clover-leaf'' lattice QCD action. The interest of using this action in Monte
Carlo simulations lies in the fact that all terms which in the continuum limit
are effectively of order $a$ ($a$ being the lattice spacing) have been
demonstrated to be absent from on-shell hadronic lattice matrix elements. We
have limited our computations to the quenched case, in which quark operators do
not mix with gluon operators.
  We have studied the transformation properties under the hypercubic group of
the operators up to the rank five (which are related to moments up to the
fourth of DIS structure functions), and we discuss the choice of the operators
considered in this paper together with the feasibility of lattice computations
for operators of higher ranks.
  To perform the huge amount of calculations required for the evaluation of all
the relevant Feynman diagrams, we have extensively used the symbolic
manipulation languages Schoonschip and Form.
