Abstract
An asymptotic formula is obtained for the number of integer solutions of bounded height on Vinogradov’s quadric. Two leading terms are determined, and a strong estimate for the error term is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brüdern J.: Einführung in die Analytische Zahlentheorie. Springer, Berlin (1995)
Greaves G.: Some diophantine equations with almost all solutions trivial. Mathematika 44, 14–36 (1997)
Rogovskaya, N.N.: An asymptotic formula for the number of solutions of a system of equations. (Russian) Diophantine Approximations, Part II (Russian), pp. 78–84. Moskov. Gos. Univ., Moscow (1986)
Skinner C.M., Wooley T.D.: On the paucity of non-diagonal solutions in certain diagonal diophantine systems. Q. J. Math. Oxf. 48(2), 255–277 (1997)
Titchmarsh, E.C.: The Theory of the Riemann Zeta-Function, 2nd edn. revised by D.R. Heath-Brown. Clarendon Press, Oxford (1986)
Vaughan R.C.: The Hardy-Littlewood Method, 2nd edn. Cambridge University Press, London (1997)
Vaughan R.C., Wooley T.D.: A special case of Vinogradov’s mean value theorem. Acta Arith. 79, 193–204 (1997)
Vaughan R.C., Wooley T.D.: On a certain nonary cubic form and related equations. Duke Math. J. 80, 669–735 (1995)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. Schoißengeier.
Rights and permissions
About this article
Cite this article
Blomer, V., Brüdern, J. The number of integer points on Vinogradov’s quadric. Monatsh Math 160, 243–256 (2010). https://doi.org/10.1007/s00605-008-0085-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-008-0085-8