About Dirichle's rows whith finite-valued multiplicative coefficients, satisfy the Riman's type functional equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 13-15
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In this paper the class of absolutely convergent on the half-plane $\sigma>1$ Dirichlet series with multiplicative finite-valued coefficients is considered. We prove that only Dirichlet $L$-functions are solutions of a functional Riemann type equation.
[1] Chandrasekkharan K., Arifmeticheskie funktsii, Nauka, M., 1975, 272 pp. | MR
[2] Voronin S. I., Karatsuba A. A., Dzeta-funktsiya Rimana, Fizmatgiz, M., 1994, 376 pp. | MR
[3] Kuznetsov V. N., Setsinskaya E. V., Krivobok V. V., “O ryadakh Dirikhle, opredelyayuschikh tselye funktsii pervogo poryadka”, Issledovaniya po algebre, teorii chisel, funktsionalnomu analizu i smezhnym voprosam: Mezhvuz. sb. nauch. tr., 3, Saratov, 2005, 47–58
[4] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1967, 239 pp. | MR
[5] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1967, 511 pp. | MR