Abstract
is well known that the Hurwitz zeta function ζ(s, α) with rational or transcendental parameter α is universal in the sense of Voronin, i.e., a wide class of analytic functions can be approximated by the shifts ζ(s + iτ, α), τ ∈ ℝ. The case of algebraic irrational α is still an open problem. It is proved that there exists a nonempty closed set of analytic functions that can be approximated by shifts ζ(s + iτ, α) with algebraic irrational α.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. N. Voronin, Analytic Properties of Generating Dirichlet Functions of Arithmetical Objects, Doctoral (Phys.–Math. ) Dissertation (MIAN,Moscow, 1977) [in Russian].
S. M. Gonek, Analytic Properties of Zeta and L–Functions, Ph. D. Thesis (Univ. ofMichigan, 1979).
B. Bagchi, The Statistical Behavior and Universality Properties of the Riemann Zeta–Function and Other Allied Dirichlet Series (Thesis, Indian Statistical Institute, 1981).
A. Laurinčikas and R. Garunkštis, The Lerch Zeta–Function (Kluwer, Kluwer Acad. Publ., 2002).
A. Laurinčikas, “On the joint universality of Hurwitz zeta–functions,” Sˇ iauliaiMath. Semin. 3 (11), 169–187 (2008).
J. W. S. Cassels, “Footnote to a note ofDavenport and Heilbronn,” J. London Math. Soc. 36, 177–184 (1961).
P. Billingsley, Convergence of ProbabilityMeasures (JohnWiley & Sons, New York, 1968).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © A. Balčiūnas, A. Dubickas, A. Laurinčikas, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 2, pp. 179–186.
Rights and permissions
About this article
Cite this article
Balčiūnas, A., Dubickas, A. & Laurinčikas, A. On the Hurwitz Zeta Functions with Algebraic Irrational Parameter. Math Notes 105, 173–179 (2019). https://doi.org/10.1134/S0001434619010218
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434619010218