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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.

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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
\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
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 443--453

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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
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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
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    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
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    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
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    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
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    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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    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
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