Abstract
One obtains asymptotic formulas for the number of solutions of the equation n= f(x,y,z)+w2k, 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)=x2+y2+z2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
C. Holley, “On Waring's problem for two squars and three cubes,” J. Reine Angew. Math.,328, 161–207 (1981).
C. Hooley, “On a new approach to various problems of Waring's type,” in: Recent Progress in Analytic Number Theory. Vol. 1 (Durham, 1979), Academic Press, London (1981), pp. 127–191.
H. L. Montogemery, Topics in Multiplicative Number Theory, Lecture Notes in Math., No. 227, Springer, Berlin (1971).
A. V. Malyshev, “Representation of integers by positive quadratic forms,” Trudy Mat. Inst. Akad. Nauk SSSR,65 (1962).
E. V. Podsypanin, “The number of integral points in an elliptic region (a remark on a theorem of A. V. Malyshev),” J. Sov. Math.,18, No. 6 (1982).
P. Deligne, “La conjecture de Weil. I,” Inst. Hautes Etudes Sci. Publ. Math.,43, 272–307 (1974).
G. A. Lomadze, “On the representation of numbers by positve ternary diagonal quadratic forms. I, II,” Acta Arith.,19, No. 3, 267–305; No. 4, 387–407 (1971).
E. P. Golubeva, “The asymptotic distribution of lattice points, belonging to given residue classes, on hyperboloids of a special form,” Mat. Sb.,123 (165), No. 4, 510–533 (1984).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 27–37, 1985.
Rights and permissions
About this article
Cite this article
Golubeva, E.P. Waring's problem for a ternary quadratic form and an arbitrary even power. J Math Sci 38, 2045–2054 (1987). https://doi.org/10.1007/BF01474437
Issue Date:
DOI: https://doi.org/10.1007/BF01474437