Geodesic
The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form
Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 507-532

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Under the assumption of a nontrivial shift of the zeros of Dirichlet $L$-series with quadratic character, asymptotic formulas are obtained for the number of lattice points in arbitrary regions on the hyperboloid $n=A\mathbf b^2+\mathbf{ac}$ belonging to given residue classes. A method for applying the results to the study of the distribution of lattice points on general second-order surfaces is outlined. Bibliography: 19 titles. 
@article{SM_1985_51_2_a11,
     author = {E. P. Golubeva},
     title = {The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form},
     journal = {Sbornik. Mathematics},
     pages = {507--532},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_51_2_a11/}
}
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E. P. Golubeva. The asymptotic distribution of lattice points belonging to given residue classes on hyperboloids of special form. Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 507-532. http://geodesic.mathdoc.fr/item/SM_1985_51_2_a11/