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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 3, Pages 79–102 (Mi izv2771)  

This article is cited in 29 scientific papers (total in 29 papers)

Joint universality of zeta-functions with periodic coefficients

A. Laurinčikas

Vilnius University

Abstract: We obtain a joint universality theorem of Voronin type for a set of functions consisting of periodic zeta-functions and periodic Hurwitz zeta-functions with algebraically independent parameters.

Keywords: periodic zeta-function, periodic Hurwitz zeta-function, limit theorem, joint universality.

DOI: https://doi.org/10.4213/im2771

Full text: PDF file (612 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:3, 515–539

Bibliographic databases:

UDC: 511
MSC: 11M35
Received: 15.02.2008
Revised: 06.08.2008

Citation: A. Laurinčikas, “Joint universality of zeta-functions with periodic coefficients”, Izv. RAN. Ser. Mat., 74:3 (2010), 79–102; Izv. Math., 74:3 (2010), 515–539

Citation in format AMSBIB
\by A.~Laurin{\v{c}}ikas
\paper Joint universality of zeta-functions with periodic coefficients
\jour Izv. RAN. Ser. Mat.
\yr 2010
\vol 74
\issue 3
\pages 79--102
\jour Izv. Math.
\yr 2010
\vol 74
\issue 3
\pages 515--539

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  • https://doi.org/10.4213/im2771
  • http://mi.mathnet.ru/eng/izv/v74/i3/p79

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    This publication is cited in the following articles:
    1. Laurincikas A., “Joint Discrete Universality For Periodic Zeta-Functions. II”, Quaest. Math.  crossref  isi
    2. Laurincikas A., “Joint Discrete Universality For Periodic Zeta-Functions. III”, Quaest. Math.  crossref  mathscinet  isi
    3. Genys J., Macaitienė R., Račkauskienẹ S., Šiaučiūnas D., “A mixed joint universality theorem for zeta-functions”, Math. Model. Anal., 15:4 (2010), 431–446  crossref  mathscinet  zmath  isi  scopus
    4. Antanas Laurinčikas, Renata Macaitienė, Darius Šiaučiūnas, “Joint universality for zeta-functions of different types”, Chebyshevskii sb., 12:2 (2011), 192–203  mathnet  mathscinet
    5. Laurinčikas A., “On joint universality of the Riemann zeta-function and Hurwitz zeta-functions”, J. Number Theory, 132:12 (2012), 2842–2853  crossref  mathscinet  zmath  isi  scopus
    6. Janulis K., Laurinčikas A., Macaitienė R., Šiaučiūnas D., “Joint universality of Dirichlet $L$-functions and periodic Hurwitz zeta-functions”, Math. Model. Anal., 17:5 (2012), 673–685  crossref  mathscinet  zmath  isi  scopus
    7. Laurinčikas A., Šiaučiūnas D., “A mixed joint universality theorem for zeta-functions. III”, Analytic and Probabilistic Methods in Number Theory, eds. Laurincikas A., Manstavicius E., Stepanauskas G., Tev Ltd, 2012, 185–195  mathscinet  zmath  isi
    8. R. Kačinskaitė, “Universality of various zeta-functions”, Electronic Notes in Discrete Mathematics, 43 (2013), 129–135  crossref  scopus
    9. Laurinčikas A., Macaitienė R., “Joint universality of the Riemann zeta-function and Lerch zeta-functions”, Nonlinear Anal. Model. Control, 18:3 (2013), 314–326  mathscinet  zmath  isi
    10. V. Pocevičienė, D. Šiaučiūnas, “A mixed joint universality theorem for zeta-functions. II”, Math. Model. Anal., 19:1 (2014), 52–65  crossref  mathscinet  isi  scopus
    11. A. Laurinčikas, R. Macaitienė, “The joint universality of Dirichlet $L$-functions and Lerch zeta-functions”, Siberian Math. J., 55:4 (2014), 645–657  mathnet  crossref  mathscinet  isi
    12. A. Dubickas, A. Laurinčikas, “Joint discrete universality of Dirichlet $L$-functions”, Arch. Math., 104:1 (2015), 25–35  crossref  mathscinet  zmath  isi  scopus
    13. K. Matsumoto, “A survey on the theory of universality for zeta and $L$-functions”, Number theory, Ser. Number Theory Appl., 11, ed. Kaneko M. Kanemitsu S. Liu J., World Sci. Publ., Hackensack, NJ, 2015, 95–144  mathscinet  zmath  isi
    14. A. Laurinčikas, “Universality theorems for zeta-functions with periodic coefficients”, Siberian Math. J., 57:2 (2016), 330–339  mathnet  crossref  crossref  mathscinet  isi  elib
    15. A. Laurinčikas, L. Meška, “Modification of the Mishou theorem”, Chebyshevskii sb., 17:3 (2016), 135–147  mathnet  elib
    16. Janulis K., Jurgaitis D., Laurincikas A., Macaitiene R., “Universality Theorems for Some Composite Functions”, Math. Model. Anal., 21:1 (2016), 35–46  crossref  mathscinet  isi  scopus
    17. Macaitiene R., Stoncelis M., Siauciunas D., “A Weighted Universality Theorem for Periodic Zeta-Functions”, Math. Model. Anal., 22:1 (2017), 95–105  crossref  mathscinet  isi  scopus
    18. Garbaliauskiene V., Karaliunaite J., Laurincikas A., “On Zeros of Some Combinations of Dirichlet l-Functions and Hurwitz Zeta-Functions”, Math. Model. Anal., 22:6 (2017), 733–749  crossref  mathscinet  isi
    19. Macaitiene R., Stoncelis M., Siauciunas D., “A Weighted Discrete Universality Theorem For Periodic Zeta-Functions. II”, Math. Model. Anal., 22:6 (2017), 750–762  crossref  mathscinet  isi  scopus
    20. Kacinskaite R., Kazlauskaite B., “Two Results Related to the Universality of Zeta-Functions With Periodic Coefficients”, Results Math., 73:3 (2018), UNSP 95  crossref  mathscinet  isi  scopus
    21. Antanas Laurinčikas, “Joint value distribution theorems for the Riemann and Hurwitz zeta-functions”, Mosc. Math. J., 18:2 (2018), 349–366  mathnet  crossref
    22. Kacinskaite R., Matsumoto K., “On Mixed Joint Discrete Universality For a Class of Zeta-Functions. II”, Lith. Math. J., 59:1, SI (2019), 54–66  crossref  mathscinet  isi  scopus
    23. Laurincikas A., “Joint Discrete Universality For Periodic Zeta-Functions”, Quaest. Math., 42:5 (2019), 687–699  crossref  isi
    24. A. Balčiūnas, R. Macaitienė, D. Šiaučiūnas, “Joint discrete universality for $L$-functions from the Selberg class and periodic Hurwitz zeta-functions”, Chebyshevskii sb., 20:1 (2019), 46–65  mathnet  crossref
    25. Balciunas A. Garbaliauskiene V. Karaliunaite J. Macaitiene R. Petuskinaite J. Rimkeviciene A., “Joint Discrete Approximation of a Pair of Analytic Functions By Periodic Zeta-Functions”, Math. Model. Anal., 25:1 (2020), 71–87  crossref  isi
    26. Laurincikas A., Siauciunas D., Vaiginyt A., “on Joint Approximation of Analytic Functions By Nonlinear Shifts of Zeta-Functions of Certain Cusp Forms”, Nonlinear Anal.-Model Control, 25:1 (2020), 108–125  crossref  isi
    27. A. Laurinchikas, “Sovmestnaya universalnost dzeta-funktsii s periodicheskimi koeffitsientami. II”, Sib. matem. zhurn., 61:5 (2020), 1064–1076  mathnet  crossref
    28. Kacinskaite R., Matsumoto K., “On Mixed Joint Discrete Universality For a Class of Zeta-Functions: a Further Generalization”, Math. Model. Anal., 25:4 (2020), 569–583  crossref  mathscinet  isi
    29. Laurincikas A., Siauciunas D., Vadeikis G., “A Weighted Version of the Mishou Theorem”, Math. Model. Anal., 26:1 (2021), 21–33  crossref  mathscinet  isi
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