Skip to main content
Log in

The Linnik Conjecture. I

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The Linnik conjecture is proved in the mean-square version with respect to the main parameter, namely, the length of the Linnik sum. Bibliography: 9 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Yu. V. Linnik, “Additive problems and eigenvalues of modular operators,” in: Proc. of the International Congress of Math., Stockholm (1962), pp. 270–284.

  2. H. D. Kloosterman, “On the representation of numbers in the form ax2 + by2 + cz2+dt2,” Acta Math., 49, 407–464 (1926).

    Google Scholar 

  3. A. Weil, “On some exponential sums,” Proc. Natl. Acad. Sci. USA, 34, 204–207 (1948).

    Google Scholar 

  4. A. Selberg, “On the estimation of Fourier coeficients of modular forms,” in: Proc. of Symposia in Pure Math. VIII, Amer. Math. Soc., Providence (1965), pp. 1–15.

    Google Scholar 

  5. N. V. Kuznetsov, “The Petersson conjecture for parabolic forms of weight zero and the Linnik conjecture,” Mat. Sb., 111, No. 3, 334–383 (1980).

    Google Scholar 

  6. J.-M. Deshoillers and H. Iwaniec, “Kloosterman sums and Fourier coeficients of cusp forms,” Invent. Math., 70, 219–288 (1982).

    Google Scholar 

  7. D. Goldfeld and P. Sarnak, “Sums of Kloosterman sums,” Invent. Math., 71, 243–250 (1983).

    Google Scholar 

  8. A. I. Vinogradov, “The Petersson conjecture for the zero weight. I, II,” Zap. Nauchn. Semin. POMI, 249, 118–153 (1997) (I); Internet:www.pdmi.ras.ru/preprint/1999/index/html,18 (II).

    Google Scholar 

  9. A. I. Vinogradov, “Comparison of spectra. II,” Zap. Nauchn. Semin. POMI, 236, 50–68 (1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vinogradov, A.I. The Linnik Conjecture. I. Journal of Mathematical Sciences 112, 4277–4284 (2002). https://doi.org/10.1023/A:1020330600146

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020330600146

Keywords

Navigation