ABSTRACT. An asymptotic formula for the number of points of an arbitrary lattice in the hyperbolic cross is obtained.KEY WORDS: complete lattice, polar lattice, asymptotic formulas for the number of lattice points, hyperbolic cross.

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ABSTRACT. The continuity of the hyperbolic zeta function of lattices (H(AIc=), a = #+it, o" > 1, as a function on the metric space of lattices is proved.KEY WORDS: hyperbolic zeta function, space of lattices, hyperbolic cross. The goal of the present paper is to prove the continuity of the hyperbolic zeta function of lattices on the space of lattices. In particular, the following m~n result is established.

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