Geodesic
Representation of integers by isotropic ternary quadratic forms
Izvestiya. Mathematics , Tome 70 (2006) no. 3, pp. 587-604

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The discrete ergodic method is used to find a complete solution of the problem of the asymptotic behaviour of the number of representations of integers by an arbitrary integral isotropic ternary quadratic form both over regions on the corresponding surface and over the residue classes of a given modulus. 
@article{IM2_2006_70_3_a3,
     author = {U. M. Pachev},
     title = {Representation of integers by isotropic ternary quadratic forms},
     journal = {Izvestiya. Mathematics },
     pages = {587--604},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_3_a3/}
}
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U. M. Pachev. Representation of integers by isotropic ternary quadratic forms. Izvestiya. Mathematics , Tome 70 (2006) no. 3, pp. 587-604. http://geodesic.mathdoc.fr/item/IM2_2006_70_3_a3/