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The number of integer points under a parabola

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Abstract

The remainder term for the number of integer points under the parabola in the region 0 < x ≤ b ≤a, 0 < y ≤ x2/a admits a boundo(a1/x+c/Inina) with the unimprovable exponent 1/2.

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Literature cited

  1. I. M. Vinogradov, Foundations of Number Theory [in Russian], Nauka, Moscow (1972).

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  3. I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory [in Russian], Nauka, Moscow (1971).

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  4. K. Prakhar, The Distribution of Prime Numbers [in Russian], Mir, Moscow (1967).

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Authors and Affiliations

  1. Leningrad division of the Steklov Mathematical Institute, Academy of Sciences of the SSSR, USSR

    V. N. Popov

Authors
  1. V. N. Popov
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Additional information

Translated from Matematicheskie Zametki, Vol. 18, No. 5, pp. 699–704, November, 1975.

The author is grateful to A. I. Vinogradov and O. M. Fomenko for their discussions.

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Popov, V.N. The number of integer points under a parabola. Mathematical Notes of the Academy of Sciences of the USSR 18, 1007–1010 (1975). https://doi.org/10.1007/BF01153567

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