Skip to main content
Log in

Estimation on curves of Dirichlet series with a convex growth majorant

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

For a class of Dirichlet series defined by a certain convex growth majorant we establish conditions for a sequence of indices which provide the implementation of precise estimates for their increase and decrease on curves that tend to infinity in a special way.

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

    Article  MATH  MathSciNet  Google Scholar 

  2. A. M. Gaisin and I.D. Latypov, “Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves,” Matem. Zametki 78(1), 37–51 (2005).

    MathSciNet  Google Scholar 

  3. A. F. Leont’ev, Sequences of Exponential Polynomials (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  4. A. M. Gaisin, “Estimates of the Growth and Decrease on Curves of an Entire Function of Infinite Order,” Matem. Sborn. 194(8) 55–82 (2002).

    MathSciNet  Google Scholar 

  5. N. N. Yusupova, “Stability of the Maximal Term of the Dirichlet Series Taken in the Logarithmic Form,” in Scientific traineeship of young researchers “Modern Informational and Computer Technology in Engineer-Scientific Research,” Vol. I, Part 2 (Ufa, RIO BashGU, 2005), pp. 309–315.

    Google Scholar 

  6. W. K. Hayman, Meromorphic Functions (Clarendon Press, Oxford, 1964; Mir, Moscow, 1966).

    MATH  Google Scholar 

  7. A. M. Gaisin, “On a Conjecture of Pólya,” Izv. RAN. Ser. Matem. 58(2) 73–92 (1994).

  8. S. Mandelbrojt, Séries Adhérent. Régularisation des Suites. Applications (Gauthier-Villars, Paris, 1952; Inostr. Lit., Moscow, 1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. N. Yusupova.

Additional information

Original Russian Text © N.N. Yusupova, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 5, pp. 45–54.

About this article

Cite this article

Yusupova, N.N. Estimation on curves of Dirichlet series with a convex growth majorant. Russ Math. 53, 38–47 (2009). https://doi.org/10.3103/S1066369X09050053

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X09050053

Key words and phrases

Navigation