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Asymptotic number of points on certain ellipsoids

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Abstract

We obtain an asymptotic formula for the number of integral representations of large numbers by ternary positive quadratic forms of a special type, assuming a boundary of zeros of Dirichlet L-functions with real characters.

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Literature cited

  1. Yu. V. Linnik, Ergodic Properties of Algebraic Fields, Vol. 45, Springer-Verlag, Berlin (1968).

    Google Scholar 

  2. A. V. Malyshev, “On the representation of integers by positive quadratic forms,” Trudy Matem. inta, Akad. Nauk SSSR,45, 1–315 (1962).

    Google Scholar 

  3. N. G. Chudakov, Introduction to the Theory of Dirichlet L-functions [in Russian], Moscow (1947).

  4. E. Hekke, “Eine neue Art von Zetafunctionen und ihre Beziehungen zur Verteilung der Primzahlen zweite Mitteilung,” Math. Zeitschr.,6, 11–51 (1920).

    Google Scholar 

  5. M. B. Barban and P. P. Vekhov, “Summation of multiplicative functions of polynomials,” Matem. Zametki,5, No. 6, 669–680 (1969).

    Google Scholar 

  6. A. I. Vinogradov and Yu. V. Linnik, “An estimate of the sum of the number of divisors in a short interval of arithmetic progression,” Uspekhi Matem. Nauk,12, No. 4, 277–280 (1957).

    Google Scholar 

  7. A. I. Vinogradov, “On numbers with small prime divisors,” Dokl. Akad. Nauk SSSR,105, No. 4, 683–686 (1956).

    Google Scholar 

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Leningrad Branch, Academy of Sciences of the USSR, USSR

    E. P. Golubeva

Authors
  1. E. P. Golubeva
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Additional information

Translated from Matematicheskie Zametki, Vol. 11, No. 6, pp. 625–634, June, 1972.

In conclusion I wish to thank A. I. Vinogradov for his interest in this paper.

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Golubeva, E.P. Asymptotic number of points on certain ellipsoids. Mathematical Notes of the Academy of Sciences of the USSR 11, 381–386 (1972). https://doi.org/10.1007/BF01093722

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  • DOI: https://doi.org/10.1007/BF01093722

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