Skip to main content
Log in

Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.

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. Gaisin A. M. and Belous T. I., “B-Stability of the maximal term of the Hadamard composition of two Dirichlet series,” Sibirsk. Mat. Zh., 43, No. 6, 1271–1282 (2002).

    Google Scholar 

  2. Pólya G., “Untersuchungen über Lücken und Singularitäten von Potenzeihen,” Math. Z., 29, 549–640 ( 1929).

    Google Scholar 

  3. Fuchs W. H. J., “Proof of a conjecture of G. Pólya concerning gap series,” Illinois J. Math., 7, 661–667 (1963).

    Google Scholar 

  4. Kövari T., “On the asymptotic paths of entire functions with gap power series,” J. Anal. Math., 15, 281–286 (1965).

    Google Scholar 

  5. Hayman W. K., “Angular value distribution of power series with gaps,” Proc. London Math. Soc., 24, 590–624 (1972).

    Google Scholar 

  6. Pavlov A. I., “On the growth over curves for entire functions given by gap power series,” Sibirsk. Mat. Zh., 13, No. 5, 1169–1181 (1972).

    Google Scholar 

  7. Korevaar J. and Dixon M., “Interpolation, strongly nonspanning powers and Macintyre exponents,” Indag. Math. (N. S.), 40, No. 2, 243–258 (1978).

    Google Scholar 

  8. Gaísin A. M., “Strong incompleteness of a system of exponentials and a problem of Macintyre,” Mat. Sb., 182, No. 7, 931–945 (1991).

    Google Scholar 

  9. Gaísin A. M., “Asymptotic estimate of the sum of a Dirichlet series over curves,” Mat. Zametki, 61, No. 6, 810–816 (1997).

    Google Scholar 

  10. Gaísin A. M., “An estimate for a Dirichlet series with Fejér gaps over curves,” Dokl. Akad. Nauk, 370, No. 6, 735–737 (2000).

    Google Scholar 

  11. Leont 'ev A. F., Series of Exponentials [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  12. Gaísin A. M., “Behavior of the logarithm of the modulus of the sum of a Dirichlet series convergent in a half-plane,” Izv. Ross. Akad. Nauk Ser. Mat., 53, No. 4, 173–185 (1994).

    Google Scholar 

  13. Skaskiv O. B., “On Wiman's theorem concerning the minimum modulus of a function analytic in the unit disk,” Izv. Akad. Nauk SSSR Ser. Mat., 53, No. 4, 833–850 (1989).

    Google Scholar 

  14. Beurling A., “Some theorems on boundedness of analytic functions,” Duke Math. J., 16, 355–359 (1949).

    Google Scholar 

  15. Hayman W. K., “How quickly can an entire function tend to zero along a curve?” Enseign. Math., 24, No. 3–4, 215–223 (1978).

    Google Scholar 

  16. Evgrafov M. A., Asymptotic Estimates and Entire Functions [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  17. Leont 'ev A. F., Sequences of Polynomials of Exponentials [in Russian], Nauka, Moscow (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaīsin, A.M., Belous, T.I. Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane. Siberian Mathematical Journal 44, 22–36 (2003). https://doi.org/10.1023/A:1022004102200

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022004102200

Navigation