Geodesic
Functional Independence of Periodic Hurwitz Zeta Functions
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 69-76.

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We prove functional independence and joint functional independence for a set of Hurwitz zeta functions with periodic coefficients and parameters algebraically independent over the field of rational numbers.
Keywords: periodic Hurwitz zeta function, meromorphic function, functional independence, Dirichlet character, Dirichlet $L$-function, Dedekind zeta function, algebraically independent members. 
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A. P. Laurincikas. Functional Independence of Periodic Hurwitz Zeta Functions. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a7/

[1] Problemy Gilberta: Sb., ed. P. S. Aleksandrov, Nauka, M., 1969 | MR

[2] A. Ostrowski, “Über Dirichletsche Reihen und algebraische Differentialgleichungen”, Math. Z., 8:3–4 (1920), 241–298 | DOI | MR | Zbl

[3] A. G. Postnikov, “O differentsialnoi nezavisimosti ryadov Dirikhle”, Dokl. AN SSSR, 66:4 (1949), 561–564 | MR | Zbl

[4] A. G. Postnikov, “Obobschenie odnoi iz zadach Gilberta”, Dokl. AN SSSR, 107:4 (1956), 512–515 | MR | Zbl

[5] S. M. Voronin, “O differentsialnoi nezavisimosti $\zeta$-funktsii”, Dokl. AN SSSR, 209:6 (1973), 1264–1266 | MR | Zbl

[6] S. M. Voronin, A. A. Karatsuba, Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 | MR | Zbl

[7] S. M. Voronin, Izbrannye trudy: Matematika, ed. A. A. Karatsuba, MGTU im. N. E. Baumana, 2006

[8] S. M. Voronin, “O funktsionalnoi nezavisimosti $L$-funktsii Dirikhle”, Acta Arith., 27 (1975), 493–503 | MR | Zbl

[9] A. Laurinčikas, “Distribution de values de certaines séries de Dirichlet”, C. R. Acad. Sci. Paris. Sér. A, 289 (1979), 43–45 | MR | Zbl

[10] A. Laurinčikas, “Sur les séries de Dirichlet et les polynômes trigonométriques”, Séminaire de Théorie des Nombres, 1978–1979, Exp. No 24, CNRS, Talence | MR | Zbl

[11] A. P. Laurinchikas, “Raspredelenie znachenii proizvodyaschikh ryadov Dirikhle multiplikativnykh funktsii”, Litovskii matem. sb., 22:1 (1982), 101–111 | MR | Zbl

[12] A. Laurinčikas, Limit theorems for the Riemann zeta-function, Math. Appl., 352, Kluwer Acad. Publ., Dordrecht, 1996 | MR | Zbl

[13] A. Reich, “Zetafunktionen und Differenzen-Differentialgleichungen”, Arch. Math. (Basel), 38 (1982), 226–235 | DOI | MR | Zbl

[14] R. Garunkštis, A. Laurinčikas, “On one Hilbert's problem for the Lerch zeta-function”, Publ. Inst. Math. (Beograd) (N.S.), 65 (79) (1999), 63–68 | MR | Zbl

[15] R. Garunkštis, A. Laurinčikas, “The Lerch zeta-function”, Analytical methods of analysis and differential equations (Minsk, 1999), Integral Transform. Spec. Funct., 10:3–4 (2000), 211–226 | DOI | MR | Zbl

[16] A. Laurinčikas, K. Matsumoto, “The joint universality and the functional independence for Lerch zeta-functions”, Nagoya Math. J., 157 (2000), 211–227 | MR | Zbl

[17] A. Laurinčikas, R. Garunkštis, The Lerch Zeta-Function, Kluwer Acad. Publ., Dordrecht, 2002 | MR | Zbl

[18] A. Laurinčikas, K. Matsumoto, “Joint value-distribution theorems on Lerch zeta-functions. II”, Liet. Mat. Rink., 46:3 (2006), 332–350 | MR | Zbl

[19] A. Laurinčikas, K. Matsumoto, “Joint value-distribution theorems on Lerch zeta-functions. III”, Proc. 4-th Palanga Conf. (to appear)

[20] V. Garbaliauskienė, A. Laurinčikas, “Some analytic properties for $L$-functions of elliptic curves”, Tr. in-ta matem. NAN Belarusi, 13:1 (2005), 1–8

[21] J. Steuding, Value-distribution of $L$-functions and allied zeta-functions – with an emphasis on aspects of universality, Habilitationsschrift, J. W. Goethe-Universität, Frankfurt, 2003

[22] A. Laurinchikas, Sovmestnaya universalnost periodicheskikh dzeta-funktsii Gurvitsa, preprint, Vilnyusskii universitet, 2006

[23] S. M. Voronin, “Teorema o raspredelenii znachenii dzeta-funktsii Rimana”, Dokl. AN SSSR, 221:4 (1975), 771 | MR | Zbl

[24] S. M. Voronin, “Teorema ob “universalnosti” dzeta-funktsii Rimana”, Izv. AN SSSR. Ser. matem., 39:3 (1975), 475–486 | MR | Zbl