64
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On Zeros of Some Combinations of Dirichlet L-Functions and Hurwitz Zeta-Functions

, &
Pages 733-749 | Received 04 Jun 2017, Published online: 27 Nov 2017

References

  • B. Bagchi. The Statistical Behaviuor and Universality Properties of the Riemann Zeta-Function and Other Allied Dirichlet Series. PhD Thesis, Indian Statistical Institute, Calcutta, 1981.
  • B. Bagchi. A joint universality theorem for Dirichlet L-functions. Math. Z., 181(3):319–334, 1982. https://doi.org/10.1007/BF01161980.
  • P. Billingsley. Convergence of Probability Measures. Willey, New York, 1968.
  • J.W.S. Cassels. Footnote to a note of Davenport and Heilbronn. J. London Math. Soc., 36:177–184, 1961. https://doi.org/10.1112/jlms/s1-36.1.177.
  • H. Davenport and H. Heilbronn. On the zeros of certain Dirichlet series I. J. London Math. Soc., 11:181–185, 1936. doi: 10.1112/jlms/s1-11.3.181
  • S.M. Gonek.: Analytic Properties of Zeta and L-Functions. PhD Thesis, University of Michigan, 1979.
  • A. Javtokas and A. Laurinčikas. On the periodic Hurwitz zeta-function. Hardy-Ramanujan J., 29:18–36, 2006.
  • A. Laurinčikas. Limit Theorems for the Riemann Zeta-Function. Kluwer Academic Publishers, Dordrecht, Boston, London, 1996.
  • A. Laurinčikas. The joint universality of Hurwitz zeta-functions. Šiauliai Math. Semin., 3 (11):169–187, 2008.
  • A. Laurinčikas. Joint universality of zeta-functions with periodic coefficients. Izvestiya: Mathematics, 74(3):515–539, 2010. https://doi.org/10.1070/IM2010v074n03ABEH002497.
  • A. Laurinčikas. On joint universality of Dirichlet L-functions. Chebyshevskii Sb., 12(1):124–139, 2011.
  • A. Laurinčikas. Joint universality of Hurwitz zeta-functions. Bull. Aust. Math. Soc., 86:232–243, 2012. https://doi.org/10.1017/S0004972712000342.
  • A. Laurinčikas. Universality of composite functions. RIMS Kôkyôroku Bessatsu, B34:191–204, 2012.
  • A. Laurinčikas and R. Garunkštis. The Lerch Zeta-Function. Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
  • A. Laurinčikas and D. Šiaučiūnas. Remarks on the universality of periodic zeta-function. Math. Notes, 80(3–4):711–722, 2006. doi: 10.1007/s11006-006-0171-y
  • S.N. Mergelyan. Uniform approximations to functions of complex variable. Usp. Mat. Nauk., 7:31–122, 1952 (in Russian).
  • A. Mikalajūnaitė. Joint universality of Dirichlet L-functions. Master thesis, Vilnius University, Faculty of Mathematics and Informatics, Vilnius, 2012 (in Lithuanian).
  • T. Nakamura and Ł. Pańkowski. On universality for linear combinations of L-functions. Monatsh. Math., 165:433–446, 2012. https://doi.org/10.1007/s00605-011-0283-7.
  • T. Nakamura and Ł. Pańkowski. On complex zeros off the critical line for non-monomial polynomial of zeta-functions. Math. Z., 284:23–39, 2016. https://doi.org/10.1007/s00209-016-1643-8.
  • J. Steuding.: Value-Distribution of L-Functions. Lect. Notes. Math. Vol. 1877, Springer-Verlag, Berlin, Heidelberg, 2007.
  • S.M. Voronin.: On the functional independence of Dirichlet L-functions. Acta Arith., 27:493–503, 1975 (in Russian). doi: 10.4064/aa-27-1-493-503
  • S.M. Voronin. Analytic Properties of Generating Function of Arithmetic Objects. Diss. doktor fiz.-matem. nauk, Moscow, 1977 (in Russian).
  • S.M. Voronin. Collected Works. Mathematics. A.A. Karatsuba (Ed.), Izd. MGTU im. N. E. Baumana, Moscow, 2006 (in Russian).
  • J.L. Walsh. Interpolation and Approximation by Rational Functions in the Complex Domain. Amer. Math. Soc. Colloq. Publ., Vol. 20, 1960.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.