Geodesic
On the Functional Independence of Zeta-Functions of Certain Cusp Forms
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 550-560.

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The zeta-function $\zeta(s,F)$, $s=\sigma+it$ of a cusp form $F$ of weight $\kappa$ in the half-plane $\sigma>(\kappa+1)/2$ is defined by the Dirichlet series whose coefficients are the coefficients of the Fourier series of the form $F$. The compositions $V(\zeta(s,F))$ with an operator $V$ on the space of analytic functions are considered, and the functional independence of these compositions for certain classes of operators $V$ is proved.
Keywords: zeta-function of a cusp form, functional independence, Hecke eigen-cusp form, universality. 
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A. Laurinčikas. On the Functional Independence of Zeta-Functions of Certain Cusp Forms. Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 550-560. http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a5/

[1] O. Hölder, “Über die Eigenschaft der Gammafunktion keiner algebraischen Differentialgleichung zu genügen”, Math. Ann., 28 (1887), 1–13 | DOI

[2] D. Gilbert, “Doklad na Matematicheskom kongresse 1900 g.”, Problemy Gilberta, Nauka, M., 1969

[3] D. D. Mordukhai-Boltovskii, “O zadache Gilberta”, Izv. Varshavskogo politekh. in-ta, 2 (1914), 1–16

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

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

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

[7] S. M. Voronin, “O differentsialnoi nezavisimosti $\zeta$-funktsii”, Dokl. AN SSSR, 206:6 (1973), 1264–1266 | MR

[8] S. M. Voronin, Izbrannye trudy. Matematika, Izd-vo MGTU im. N. E. Baumana, M., 2006

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

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

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

[12] A. Laurinchikas, K. Matsumoto, I. Steuding, “Universalnost $L$-funktsii, svyazannykh s novymi formami”, Izv. RAN. Ser. matem., 67:1 (2003), 83–98 | DOI | MR | Zbl

[13] A. Laurinčikas, Limit Theorems for the Riemann Zeta-Function, Kluwer Acad. Publ., Dordrecht, 1996 | MR

[14] A. Laurinčikas, K. Matsumoto, “The universality of zeta-functions attached to certain cusp forms”, Acta Arith., 98:4 (2001), 345–359 | DOI | MR

[15] A. Laurinčikas, K. Matsumoto, J. Steuding, “Universality of some functions related to zeta-functions of certain cusp forms”, Osaka J. Math., 50:4 (2013), 1021–1037 | MR