View More View Less
  • 1 Šiauliai University Department of Mathematics, Faculty of Mathematics and Informatics Višinskio 19 LT-77156 Šiauliai Lithuania
  • | 2 Vilnius University Department of Probability Theory and Number Theory, Faculty of Mathematics and Informatics Naugarduko 24 LT-03225 Vilnius Lithuania
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

In this paper, the joint approximation of a given collection of analytic functions by a collection of shifts of zeta-functions with periodic coefficients is obtained. This is applied to prove the functional independence for these zeta-functions.

  • Bagchi, B., The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, PhD Thesis, Calcutta, Indian Statistical Institute, 1981.

    Bagchi B. , '', in The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series , (1981 ) -.

  • Bagchi, B., Joint universality theorem for Dirichlet L-functions, Math. Z., 181 (1982), 319–334. MR 0678888 (84c:10083)

    Bagchi B. , 'Joint universality theorem for Dirichlet L-functions ' (1982 ) 181 Math. Z. : 319 -334.

    • Search Google Scholar
  • Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968.

    Billingsley P. , '', in Convergence of Probability Measures , (1968 ) -.

  • Conway, J. B., Functions of One Complex Variable. I, Springer-Verlag, New York, 1978. MR 0503901 80c:30003

    Conway J. B. , '', in Functions of One Complex Variable. I , (1978 ) -.

  • Cramér, H. and Leadbetter, M. R., Stationary and Related Stochastic Processes, Wiley, New York, 1967. MR 0217860 36#949

    Leadbetter M. R. , '', in Stationary and Related Stochastic Processes , (1967 ) -.

  • Garunkštis, R. and Laurinčikas, A., On one Hilbert’s problem for the Lerch zetafunction, Publ. Inst. Math., 65(79) (1999), 63–69. MR 1717402 2000i:11134

    Laurinčikas A. , 'On one Hilbert’s problem for the Lerch zetafunction ' (1999 ) 65 Publ. Inst. Math. : 63 -69.

    • Search Google Scholar
  • Gonek, S. M., Analytic properties of zeta and L-functions, PhD Thesis, University of Michigan, 1979.

  • Hayer, H., Probability Measures on Locally Compact Groups, Springer-Verlag, 1977.

  • Hölder, O., Über die Eigenschaft der Gamafunktion keiner algebraischen Differentialgleichung zu genügen, Math. Ann., 28 (1887), 1–13.

    Hölder O. , 'Über die Eigenschaft der Gamafunktion keiner algebraischen Differentialgleichung zu genügen ' (1887 ) 28 Math. Ann. : 1 -13.

    • Search Google Scholar
  • Javtokas, A. and Laurinficikas, A., On the periodic Hurwitz zeta-function, Hardy-Ramanujan J., 29 (2006), 18–36. MR 2278304 2007j:11113

    Laurinficikas A. , 'On the periodic Hurwitz zeta-function ' (2006 ) 29 Hardy-Ramanujan J. : 18 -36.

    • Search Google Scholar
  • Laurinčikas, A., Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht, Boston, London, 1996. MR 1376140 96m:11070

    Laurinčikas A. , '', in Limit Theorems for the Riemann Zeta-Function , (1996 ) -.

  • Laurinčikas, A., The universality of zeta-funtions, Acta Appl. Math., 78 (2003), 251–271. MR 2024030 2005a:11136

    Laurinčikas A. , 'The universality of zeta-funtions ' (2003 ) 78 Acta Appl. Math. : 251 -271.

    • Search Google Scholar
  • Laurinčikas, A., Joint universality of general Dirichlet series, Izvestiya RAN, Ser. Matem., 69:1 (2005), 133–144 (in Russian) = Izvestiya: Mathematics, 69:1 (2005), 131–142. MR 2128183 2005k:11188

    Laurinčikas A. , 'Joint universality of general Dirichlet series ' (2005 ) 69 Izvestiya RAN, Ser. Matem. : 133 -144.

    • Search Google Scholar
  • Laurinčikas, A., An analogue of the Voronin’s theorem for periodic Hurwitz zetafunctions, Matem. Sb., 198, No. 2 (2007), 91–103 (in Russian). MR 2355443 2008j:11112

    Laurinčikas A. , 'An analogue of the Voronin’s theorem for periodic Hurwitz zetafunctions ' (2007 ) 198 Matem. Sb. : 91 -103.

    • Search Google Scholar
  • Laurinčikas, A., On joint universality of periodic Hurwitz zeta-functions, Lith. Math. J., 48, No. 1 (2008), 79–91. MR 2398173 2009e:11168

    Laurinčikas A. , 'On joint universality of periodic Hurwitz zeta-functions ' (2008 ) 48 Lith. Math. J. : 79 -91.

    • Search Google Scholar
  • Laurinčikas, A. and Garunkštis, R., The Lerch Zeta-Function, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002. MR 1979048 2004c:11161

    Garunkštis R. , '', in The Lerch Zeta-Function , (2002 ) -.

  • Laurinčikas, A. and Matsumoto, K., The joint universality and the functional independence for Lerch zeta-functions, Nagoya Math. J., 157 (2000), 211–227. MR 1752482 2001d:11089

    Matsumoto K. , 'The joint universality and the functional independence for Lerch zeta-functions ' (2000 ) 157 Nagoya Math. J. : 211 -227.

    • Search Google Scholar
  • Laurinčikas, A. and Matsumoto, K., The joint universality of twisted automorphic L-functions, J. Math. Soc. Japan, 56(3) (2004), 923–939. MR 2071679 2005h:11100

    Matsumoto K. , 'The joint universality of twisted automorphic L-functions ' (2004 ) 56 J. Math. Soc. Japan : 923 -939.

    • Search Google Scholar
  • Laurinčikas, A. and Matsumoto, K., Joint value distribution theorems on Lerch zeta-functions. II, Liet. Matem. Rink., 48, No. 3 (2006), 332–350. MR 2285347 2007h:11104

    Matsumoto K. , 'Joint value distribution theorems on Lerch zeta-functions. II ' (2006 ) 48 Liet. Matem. Rink. : 332 -350.

    • Search Google Scholar
  • Laurinčikas, A. and Šiaučiūnas, D., Remarks on the universality of the periodic zeta-function, Math. Notes, 80(3–4) (2006), 711–722. MR 2314364 2007k:11143

    Šiaučiūnas D. , 'Remarks on the universality of the periodic zeta-function ' (2006 ) 80 Math. Notes : 711 -722.

    • Search Google Scholar
  • Loève, M., Probability Theory, Van Nostrand, Toronto, 1955. MR 0066573 16,598f

    Loève M. , '', in Probability Theory , (1955 ) -.

  • Matsumoto, K., Probabilistic value-distribution theory of zeta-functions, Sugaku Expositions, 17, No. 1 (2004), 51–71. MR 2073363

    Matsumoto K. , 'Probabilistic value-distribution theory of zeta-functions ' (2004 ) 17 Sugaku Expositions : 51 -71.

    • Search Google Scholar
  • Matsumoto, K., An introduction to the value-distribution theory of zeta-functions, Šiauliai Math. Semin., 1(9) (2006), 61–83. MR 2547356

    Matsumoto K. , 'An introduction to the value-distribution theory of zeta-functions ' (2006 ) 1 Šiauliai Math. Semin. : 61 -83.

    • Search Google Scholar
  • Ostrowski, A., Über Dirichletsche reihen und algebraische Differentialgleichungen, Math. Z., 8 (1920), 241–298. MR 1544442

    Ostrowski A. , 'Über Dirichletsche reihen und algebraische Differentialgleichungen ' (1920 ) 8 Math. Z. : 241 -298.

    • Search Google Scholar
  • Steuding, J., Value-Distribution of L-Functions, Lecture Notes Math. 1877, Springer-Verlag, Berlin, Heidelberg, 2007. MR 2330696 2008m:11172

    Steuding J. , '', in Value-Distribution of L-Functions , (2007 ) -.

  • Šleževičienė, R., The joint universality for twists of Dirichlet series with multiplicative coefficients, in: Analytic and Probab. Methods in Number Theory, Proc. of the 3rd Intern. Conf. on honour of J. Kubilius, Palanga, 2001, A. Dubickas et al (eds), TEV, Vilnius, 2002, pp. 303–319. MR 1964873 2003m:11150

    Šleževičienė R. , '', in Analytic and Probab. Methods in Number Theory , (2002 ) -.

  • Voronin, S. M., Theorem on the “universality” of the Riemann zeta-function, Izv. Akad. Nauk SSSR, Ser. Matem., 39 (1975), 475–486 (in Russian) = Math. USSR, Izv., 9 (1975), 443–453. MR 0472727 57#12419

    Voronin S. M. , 'Theorem on the “universality” of the Riemann zeta-function ' (1975 ) 39 Izv. Akad. Nauk SSSR, Ser. Matem. : 475 -486.

    • Search Google Scholar
  • Voronin, S. M., The functional independence of L-functions, Acta Arith., 20 (1975), 493–503 (in Russian). MR 0366836 51#12419

    Voronin S. M. , 'The functional independence of L-functions ' (1975 ) 20 Acta Arith. : 493 -503.

    • Search Google Scholar
  • Voronin, S. M., The differential independence of ζ-functions, Sov. Math. Dokl., 14 (1973), 607–609 = Dokl. Akad. Nauk SSSR, 209 No. 6 (1973), 1264–1266 (in Russian). MR 0319914 47#8455

    Voronin S. M. , 'The differential independence of ζ-functions ' (1973 ) 14 Sov. Math. Dokl. : 607 -609.

    • Search Google Scholar
  • Walsh, J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Coll. Publ., Vol. 20, 1960. MR 0218587 36#1672a