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Application of the large sieve to the solution of additive problems of mixed type

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Abstract

A variant of the large-sieve: method, using a combination of results obtained by Lavrik, Montgomery, and Eombieri, is employed to derive asymptotic properties of the number of solutions of the equationNp+Na=n wherep is a prime ideal of some ideal class of a field K of degree n≤4, anda is a prime ideal of a class of an imaginary quadratic field.

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Literature cited

  1. B. M. Bredihin, J. V. Linnik, and N. G. Tschudakoff, Über Binäre Additive Problem Gemischter Art, Abhandlungen aus Zahlentheorie und Analysis, Berlin (1968), pp. 25–37.

  2. H. L. Montgomery, “Zeros of L-functions,” Inventiones Math.,8, No. 4, 346–354 (1969).

    Google Scholar 

  3. H. L. Montgomery, “Mean and large values of Dirichlet polynomials,” Inventiones Math.,8, No. 4, 334–345 (1969).

    Google Scholar 

  4. A. F. Lavrik, “Approximate functional equations for Dirichlet functions,” Izv. AN SSSR, Ser. Matem,32, No. 1, 134–185 (1968).

    Google Scholar 

  5. E. Bombieri, “On the large sieve,” Mathematika,12, No. 2, 201–225 (1965).

    Google Scholar 

  6. H. Hasse, “Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper,” Jahresbericht Deutsche Math. Vereinigung,35, 1–55 (1926).

    Google Scholar 

  7. C. Chevally, “Sur la théorie du corps de classes dans les corps finis et les corps locaux,” Journal of the Faculty of Science, Imperial Univer. of Tokyo,2, No. 9, 365–476 (1933).

    Google Scholar 

  8. H. Weyl, Algebraic Theory of Numbers, Princeton University Press, Princeton (1940).

    Google Scholar 

  9. E. K. Fogels, “The large sieve,” Izv. AN Latv. SSR, Ser. Fizich. i Tekhnich. Nauk, No. 4, 3–14 (1969).

    Google Scholar 

  10. E. Fogels, “On the zeros of Hecke's L-functions I,” Acta Arithm.,7, No. 2, 87–106 (1962).

    Google Scholar 

  11. A. I. Vinogradov, “A generalization of Klosterman's formula,” Dokl. Akad. Nauk SSSR,146, No. 4, 754–756.

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

  13. M. B. Barban, “The ‘large sieve’ method with applications in number theory,” Uspekhi Matem. Nauk,21, No. 1, 51–102 (1966).

    Google Scholar 

  14. B. M. Bredikhin and Yu. V. Linnik, “The asymptotic and ergodic properties of solutions of the generalized Hardy-Littlewood equation,” Matem. Sb., Novaya Seriya,71, No. 2, 145–161 (1966).

    Google Scholar 

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Authors and Affiliations

  1. Kuibyshev Pedagogical Institute, USSR

    L. F. Kondakova

Authors
  1. L. F. Kondakova
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Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 73–81, July, 1971.

The author wishes to thank A. I. Vinogradov for his help and advice in this work.

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Kondakova, L.F. Application of the large sieve to the solution of additive problems of mixed type. Mathematical Notes of the Academy of Sciences of the USSR 10, 468–473 (1971). https://doi.org/10.1007/BF01747073

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  • DOI: https://doi.org/10.1007/BF01747073

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