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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 1, Pages 83–98 (Mi izv419)  

This article is cited in 16 scientific papers (total in 16 papers)

The universality of $L$-functions associated with new forms

A. P. Laurincikas, K. Matsumoto, J. Steuding


Abstract: We prove the universality theorem for $L$-functions of new parabolic forms. It concerns the uniform approximation of analytic functions by shifts of these $L$-functions. This theorem together with the Shimura–Taniyama conjecture (now proved) yields the universality of $L$-functions of non-singular elliptic curves over the field of rational numbers. The universality of $L$-functions implies that they are functionally independent.

DOI: https://doi.org/10.4213/im419

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English version:
Izvestiya: Mathematics, 2003, 67:1, 77–90

Bibliographic databases:

UDC: 511
MSC: 11F66, 11M41, 11K99
Received: 28.02.2002

Citation: A. P. Laurincikas, K. Matsumoto, J. Steuding, “The universality of $L$-functions associated with new forms”, Izv. RAN. Ser. Mat., 67:1 (2003), 83–98; Izv. Math., 67:1 (2003), 77–90

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Virginija Garbaliauskiene, Laurincikas Antanas, “Discrete value: Distribution of L-functions of elliptic curves”, Publ. Inst. Math. (Belgr.), 76:90 (2004), 65  crossref  mathscinet  zmath
    2. 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
    3. Mishou H., “The joint value-distribution of the Riemann zeta function and hurwitz”, Lithuanian Math. J., 47:1 (2007), 32–47  crossref  mathscinet  zmath  isi  scopus
    4. Li Hongze, Wu Jie, “The universality of symmetric power $L$-functions and their Rankin-Selberg $L$-functions”, J. Math. Soc. Japan, 59:2 (2007), 371–392  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. Antanas Laurinčikas, Renata Macaitienė, Darius Šiaučiūnas, “Joint universality for zeta-functions of different types”, Chebyshevskii sb., 12:2 (2011), 192–203  mathnet  mathscinet
    7. Laurincikas A., Macaitiene R., “On the Universality of Zeta-Functions of Certain Cusp Forms”, Analytic and Probabilistic Methods in Number Theory, eds. Laurincikas A., Manstavicius E., Stepanauskas G., Tev Ltd, 2012, 173–183  mathscinet  zmath  isi
    8. 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  mathscinet  zmath  isi
    9. A. Laurinčikas, M. Stoncelis, D. Šiaučiūnas, “On the zeros of some functions related to periodic zeta-functions”, Chebyshevskii sb., 15:1 (2014), 121–130  mathnet
    10. 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  mathscinet  zmath  isi
    11. A. Laurinčikas, R. Macaitienė, “Value distribution of twists of $L$-functions of elliptic curves”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 70–77  mathnet  crossref  crossref  isi  elib
    12. 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
    13. Laurincikas A., “Uniform Distribution Modulo 1 and the Universality of Zeta-Functions of Certain Cusp Forms”, Publ. Inst. Math.-Beograd, 100:114 (2016), 131–140  crossref  mathscinet  zmath  isi  scopus
    14. Laurincikas A., Siauciunas D., Vaiginyte A., “Extension of the Discrete Universality Theorem For Zeta-Functions of Certain Cusp Forms”, Nonlinear Anal.-Model Control, 23:6 (2018), 961–973  crossref  mathscinet  isi
    15. N. N. Dobrovolskii, M. N. Dobrovolskii, N. M. Dobrovolskii, I. N. Balaba, I. Yu. Rebrova, “Algebra ryadov Dirikhle monoida naturalnykh chisel”, Chebyshevskii sb., 20:1 (2019), 180–196  mathnet  crossref
    16. A. Laurinčikas, “On the Functional Independence of Zeta-Functions of Certain Cusp Forms”, Math. Notes, 107:4 (2020), 609–617  mathnet  crossref  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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