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On the distribution of integral points on cones

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New results on the distribution of integral points on the cones

$$ x_1^2 + x_2^2 + x_3^2 = y_1^2 + y_2^2 + y_3^2 $$

and

$$ x_1^2 + x_2^2 + x_3^2 + x_4^2 = y_1^2 + y_2^2 + y_3^2 + y_4^2 $$

are obtained. Bibliography: 14 titles.

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References

  1. O. M. Fomenko, “Distribution of lattice points on certain second order surfaces,” Zap. Nauchn. Semin. POMI, 212,164-195 (1994).

    MathSciNet  MATH  Google Scholar 

  2. M. Kühleitner and W. G. Nowak, “The average number of solutions of the Diophantine equation U 2 + V 2 = W 3 and related arithmetic functions,” Acta. Math. Hungar., 104, No. 3, 225–240 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Schinzel, “On an analytic problem considered by Sierpiński and Ramanujan,” New Trends in Probability and Statistics, Vol. 2 (Palanga, 1991), VSP, Utrecht (1992), pp. 165–171.

  4. W. Müller, “The mean square of Dirichlet series associated with automorphic forms,” Monatsh.Math., 113, No. 2, 121–159 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Müller, “The Rankin-Selberg method for nonholomorphic automorphic forms,” J. Number Theory, 51, No. 1, 48–86 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  6. Loo-Keng Hua, The Method of Trigonometric Sums and its Applications in the Number Theory [Russian translation], Moscow (1964).

  7. P. T. Bateman, “On the representations of a number as the sum of three squares,” Trans. Amer. Math. Soc., 71, No. 1, 70–101 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Saparnijazov and A. S. Fainleb, “Dispersion of sums of real characters and moments of L(1, χ),” Izv. Akad. Nauk. Uzb. SSR. Ser. Fiz.-Mat. Nauk, 19, No. 6, 24–29 (1975).

    MATH  Google Scholar 

  9. M. Jutila, “On character sums and class numbers,” J. Number Theory, 5, No. 3, 203–214 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  10. J. L. Hafner, “On the representation of summatory functions of a class of arithmetical functions,” Lect. Notes Math., 899,148-165 (1981).

    Article  MathSciNet  Google Scholar 

  11. E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., revised by D. R. Heath-Brown, New York (1986).

  12. S. Ramanujan, “Some formulae in the analytic theory numbers,” Messenger Math., 45, 81–84 (1916).

    Google Scholar 

  13. R. A. Smith, “An error term of Ramanujan,” J. Number Theory, 2, No. 1, 91–96 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Z. Walfics, Lattice Points in Multidimensional Balls [in Russian], Tbilisi (1960).

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    O. M. Fomenko

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  1. O. M. Fomenko
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Correspondence to O. M. Fomenko.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 383, 2011, pp. 193–203.

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Fomenko, O.M. On the distribution of integral points on cones. J Math Sci 178, 227–233 (2011). https://doi.org/10.1007/s10958-011-0543-z

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