Skip to main content
Log in

Lehmer's conjecture. I

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

One formulates a conjecture which contains Lehmer's conjecture as a special case and one derives an identity which is equivalent to the negation of the conjecture.

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

Literature cited

  1. D. H. Lehmer, “Ramanujan's function, “ Duke Math. J.,10, 483–492 (1943).

  2. J. P. Serre, Une interpretation des congruences relatives a la fonction τ de Ramanujan, Seminaire Delange-Pisot-Poitou (1967–1968).

  3. R. C. Gunning, Lectures on Modular Forms, Princeton Univ. Press, Princeton (1962).

    Google Scholar 

  4. E. Hecke, “Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I,” Math. Ann.,114, 1–28 (1937).

    Google Scholar 

  5. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York (1953).

    Google Scholar 

  6. E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Part I. Clarendon Press, Oxford (1962).

    Google Scholar 

  7. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1952).

  8. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York (1953).

    Google Scholar 

  9. N. V. Kuznetsov, “Spectral methods in arithmetic problems,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,76, 159–166 (1978).

    Google Scholar 

  10. N. V. Kuznetsov, “A new class of identities for the Fourier coefficients of modular forms,” Acta Arith.,27, 505–519 (1975).

    Google Scholar 

  11. N. V. Kuznetsov, Petersson's conjecture for forms of weight zero and Linnik's conjecture, Preprint No. 02, Khabarovsk Complex Sci. Res. Inst., Far Eastern Scientific Center, Khabarovsk (1978).

    Google Scholar 

  12. N. V. Kuznetsov, “The arithmetic form of Selberg's trace formula and the distribution of the norms of the primitive hyperbolic classes of the modular group,” Preprint, Khabarovsk Complex Sci. Res. Inst., Far Eastern Scientific Center, Khabarovsk (1978).

    Google Scholar 

  13. N. V. Kuznetsov, “The distribution of norms of primitive hyperbolic classes of the modular group and asymptotic formulas for the eigenvalues of the Laplace-Beltrami operator on a fundamental region of the modular group,” Dokl. Akad. Nauk SSSR,242, No. 1, 40–43 (1978).

    Google Scholar 

  14. T. Kubota, Elementary Theory of Eisenstein Series, Halsted Press, New York (1973).

    Google Scholar 

  15. R. W. Bruggeman, “Fourier coefficients of cusp forms,” Invent. Math.,45, No. 1, 1–18 (1978).

    Google Scholar 

Download references

Authors

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 52–80, 1979.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuznetsov, N.V. Lehmer's conjecture. I. J Math Sci 17, 2116–2137 (1981). https://doi.org/10.1007/BF01567591

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01567591

Navigation