Geodesic
On the Number of Integer Points Whose First Coordinates Satisfy a Divisibility Condition on Hyperboloids of a Special Form
Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 881-886

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The discrete ergodic method is applied to obtain an asymptotic expression for the number of all integer points in a given bounded domain on a three-dimensional hyperboloid of genus determined by the invariants $[w,2]$, where $w$ is odd, such that the first coordinates of these points are divisible by $w$.
Keywords: discrete ergodic method, ternary quadratic form, number of classes of binary quadratic forms, integer point on a hyperboloid, asymptotic relation. 
@article{MZM_2016_100_6_a9,
     author = {U. M. Pachev and R. A. Dokhov},
     title = {On the {Number} of {Integer} {Points} {Whose} {First} {Coordinates} {Satisfy} a {Divisibility} {Condition} on {Hyperboloids} of a {Special} {Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {881--886},
     publisher = {mathdoc},
     volume = {100},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a9/}
}
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U. M. Pachev; R. A. Dokhov. On the Number of Integer Points Whose First Coordinates Satisfy a Divisibility Condition on Hyperboloids of a Special Form. Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 881-886. http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a9/