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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 3, Pages 475–486 (Mi izv2037)  

This article is cited in 82 scientific papers (total in 83 papers)

Theorem on the “universality” of the Riemann zeta-function

S. M. Voronin


Abstract: This paper considers the question of approximating analytic functions by translations of the Riemann zeta-function.
Bibliography: 6 items.

Full text: PDF file (799 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:3, 443–453

Bibliographic databases:

UDC: 517.5
MSC: Primary 30A82; Secondary 30A16
Received: 21.08.1974

Citation: S. M. Voronin, “Theorem on the “universality” of the Riemann zeta-function”, Izv. Akad. Nauk SSSR Ser. Mat., 39:3 (1975), 475–486; Math. USSR-Izv., 9:3 (1975), 443–453

Citation in format AMSBIB
\Bibitem{Vor75}
\by S.~M.~Voronin
\paper Theorem on the ``universality'' of the Riemann zeta-function
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 3
\pages 475--486
\mathnet{http://mi.mathnet.ru/izv2037}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=472727}
\zmath{https://zbmath.org/?q=an:0315.10037|0333.30023}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 443--453
\crossref{https://doi.org/10.1070/IM1975v009n03ABEH001485}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Kanatnikov, “Cluster sets of meromorphic functions relative to sequences of compact sets”, Math. USSR-Izv., 25:3 (1985), 501–517  mathnet  crossref  mathscinet  zmath
    2. M Antoine, A Comtet, S Ouvry, J Phys A Math Gen, 23:16 (1990), 3699  crossref  mathscinet  zmath  adsnasa
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    4. K BITAR, N KHURI, H REN, “Path integrals and Voronin's theorem on the universality of the Riemann zeta function1”, Annals of Physics, 211:1 (1991), 172  crossref
    5. G. I. Arkhipov, V. I. Blagodatskikh, A. A. Bolibrukh, V. A. Iskovskikh, A. A. Karatsuba, Yu. V. Prokhorov, A. T. Fomenko, V. N. Chubarikov, I. R. Shafarevich, “Sergei Mikhailovich Voronin (obituary)”, Russian Math. Surveys, 53:4 (1998), 777–781  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Yukitaka Abe, Paolo Zappa, “Universal Functions on Complex General Linear Groups”, Journal of Approximation Theory, 100:2 (1999), 221  crossref
    7. A. P. Laurincikas, K. Matsumoto, J. Steuding, “The universality of $L$-functions associated with new forms”, Izv. Math., 67:1 (2003), 77–90  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. P. Laurincikas, K. Matsumoto, J. Steuding, “Discrete Universality of $L$-Functions for New Forms”, Math. Notes, 78:4 (2005), 551–558  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. P. Laurincikas, “Joint universality of general Dirichlet series”, Izv. Math., 69:1 (2005), 131–142  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. A. P. Laurincikas, D. Siauciunas, “Remarks on the universality of the periodic zeta function”, Math. Notes, 80:4 (2006), 532–538  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Laurinčikas A., “The joint universality for periodic Hurwitz zeta-functions”, Analysis (Munich), 26:3 (2007), 419–428  crossref  crossref  mathscinet
    12. A. P. Laurincikas, “Voronin-type theorem for periodic Hurwitz zeta-functions”, Sb. Math., 198:2 (2007), 231–242  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Mishou H., “The joint value-distribution of the Riemann zeta function and hurwitz”, Lithuanian Mathematical Journal, 47:1 (2007), 32–47  crossref  mathscinet  zmath  isi
    14. Li H., Wu J., “The universality of symmetric power L-functions and their Rankin-Selberg L-functions”, Journal of the Mathematical Society of Japan, 59:2 (2007), 371–392  crossref  mathscinet  zmath  isi
    15. Antanas Laurinčikas, Renata Macaitienė, Darius Šiaučiūnas, “The joint universality for periodic zeta-functions”, Chebyshevskii sb., 8:2 (2007), 162–174  mathnet  mathscinet  zmath
    16. V. Garbaliauskienė, J. Genys, A. Laurinčikas, “Discrete universality of the $L$-functions of elliptic curves”, Siberian Math. J., 49:4 (2008), 612–627  mathnet  crossref  mathscinet  zmath  isi  elib
    17. Javtokas A., Laurinčikas A., “A joint universality theorem for periodic Hurwitz zeta-functions”, Bull. Aust. Math. Soc., 78:1 (2008), 13–33  crossref  mathscinet  zmath  isi
    18. A. Laurinčikas, “Joint universality for periodic Hurwitz zeta-functions”, Izv. Math., 72:4 (2008), 741–760  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. A. P. Laurincikas, “Functional Independence of Periodic Hurwitz Zeta Functions”, Math. Notes, 83:1 (2008), 65–71  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. A. P. Laurincikas, R. Macaitiené, “On the Joint Universality of Periodic Zeta Functions”, Math. Notes, 85:1 (2009), 51–60  mathnet  crossref  crossref  mathscinet  isi
    21. A. Laurinčikas, “Joint universality of zeta-functions with periodic coefficients”, Izv. Math., 74:3 (2010), 515–539  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. A. Laurincikas, “On the Joint Universality of Lerch Zeta Functions”, Math. Notes, 88:3 (2010), 386–394  mathnet  crossref  crossref  mathscinet  isi
    23. Françoise Chatelin, “Numerical information processing under the global rule expressed by the Euler–Riemann ζ function defined in the complex plane”, Chaos, 20:3 (2010), 037104  crossref  elib
    24. J. Genys, R. Macaitienė, S. Račkauskienė, D. Šiaučiūnas, “A Mixed Joint Universality Theorem for Zeta-Functions”, MATH MODELLING ANAL, 15:4 (2010), 431  crossref
    25. A. Laurinčikas, “Some value-distribution theorems for periodic Hurwitz zeta-functions”, J. Math. Sci., 180:5 (2012), 581–591  mathnet  crossref  mathscinet  elib
    26. Takashi Nakamura, “The generalized strong recurrence for non-zero rational parameters”, Arch. Math, 95:6 (2010), 549  crossref
    27. Takashi Nakamura, Łukasz Pańkowski, “On universality for linear combinations of L-functions”, Monatsh Math, 2011  crossref
    28. E. Bombieri, A. Ghosh, “Around the Davenport–Heilbronn function”, Russian Math. Surveys, 66:2 (2011), 221–270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    29. R. Garunkstis, J. Steuding, “Questions around the Nontrivial Zeros of the Riemann Zeta-Function. Computations and Classifications”, Math. Modelling & Analysis, 16:1 (2011), 72  crossref
    30. Kacinskaite R., Laurincikas A., “The Joint Distribution of Periodic Zeta-Functions”, Studia Scientiarum Mathematicarum Hungarica, 48:2 (2011), 257–279  crossref  isi
    31. A. Laurinčikas, “On joint universality of Dirichlet $L$-functions”, Chebyshevskii sb., 12:1 (2011), 124–139  mathnet  mathscinet
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    37. Hidehiko Mishou, “Joint value distribution for zeta functions in disjoint strips”, Monatsh Math, 2012  crossref
    38. A. Laurinčikas, D. Šiaučiunas, “On zeros of some analytic functions related to the Hurwitz zeta-function”, Chebyshevskii sb., 13:2 (2012), 86–90  mathnet
    39. Janulis K. Laurincikas A. Macaitiene R. Siauciunas D., “Joint Universality of Dirichlet l-Functions and Periodic Hurwitz Zeta-Functions”, Math. Model. Anal., 17:5 (2012), 673–685  crossref  isi
    40. Laurincikas A. Macaitiene R., “On the Universality of Zeta-Functions of Certain Cusp Forms”, Analytic and Probabilistic Methods in Number Theory, ed. Laurincikas A. Manstavicius E. Stepanauskas G., Tev Ltd, 2012, 173–183  isi
    41. Laurincikas A. Siauciunas D., “A Mixed Joint Universality Theorem for Zeta-Functions. III”, Analytic and Probabilistic Methods in Number Theory, ed. Laurincikas A. Manstavicius E. Stepanauskas G., Tev Ltd, 2012, 185–195  isi
    42. Laurincikas A. Matsumoto K. Steuding J., “Universality of Some Functions Related to Zeta-Functions of Certain Cusp Forms”, Osaka J. Math., 50:4 (2013), 1021–1037  isi
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    56. Matsumoto K., “a Survey on the Theory of Universality For Zeta and l-Functions”, Number Theory: Plowing and Starring Through High Wave Forms, Series on Number Theory and Its Applications, 11, ed. Kaneko M. Kanemitsu S. Liu J., World Scientific Publ Co Pte Ltd, 2015, 95–144  isi
    57. A. Laurinčikas, D. Mokhov, “A discrete universality theorem for periodic Hurwitz zeta-functions”, Chebyshevskii sb., 17:1 (2016), 148–159  mathnet  elib
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    62. Laurincikas A. Matsumoto K. Steuding J., “Discrete universality of L-functions of new forms. II”, Lith. Math. J., 56:2 (2016), 207–218  crossref  mathscinet  zmath  isi  scopus
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