Geodesic
Waring's problem for a ternary quadratic form and an arbitrary even power
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 27-37

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One obtains asymptotic formulas for the number of solutions of the equation $n=f(x, y, z)+w^{2k}$, where $f$ is a primitive integral quadratic form. One gives an estimate of the remainder, having a logarithmic reducing factor in the general case and a powerlike one when $f(x ,y, z)=x^2+y^2+z^2$. 
@article{ZNSL_1985_144_a2,
     author = {E. P. Golubeva},
     title = {Waring's problem for a ternary quadratic form and an arbitrary even power},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {27--37},
     publisher = {mathdoc},
     volume = {144},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a2/}
}
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E. P. Golubeva. Waring's problem for a ternary quadratic form and an arbitrary even power. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 27-37. http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a2/