Geodesic
Analogue of the Duffin--Scheffer theorem for one class of Dirichlet series with finite-valued coefficients
Čebyševskij sbornik, Tome 19 (2018) no. 4, pp. 243-251.

Voir la notice de l'article provenant de la source Math-Net.Ru

The well-known theorem, proved by Doffin and Scheffer, states that the boundedness of a power series with finite-valued coefficients in a certain sector of the unit circle is equivalent to the periodicity of its coefficients, starting from a certain number. The paper indicates the class of Dirichlet series with finite-valued coefficients bounded in any strip of the right half-plane of the complex complex plane by a constant depending only on the height of the strip, for which an analogue of Dauffin–Scheffer theorem is proved. Earlier, an analogue of the Dauffin–Scheffer theorem was obtained by the authors for Dirichlet series with multiplicative coefficients. The method of proving this result allowed, in particular, to solve the well-known problem of generalized characters posed in 1950 by Yu.V. Linnik and N.G. Eccentric. In this paper, this technique is used to prove an analogue of the Duffin – Scheffer theorem for the indicated class of Dirichlet series with multiplicative coefficients.
Keywords: Dirichlet approximation polynomials, analytic continuation of the Dirichlet series to the complex plane, condition for periodicity of coefficients of Dirichlet series. 
@article{CHEB_2018_19_4_a12,
     author = {V. N. Kuznetsov and O. A. Matveeva},
     title = {Analogue of the {Duffin--Scheffer} theorem for one class of {Dirichlet} series with finite-valued coefficients},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {243--251},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_4_a12/}
}
TY  - JOUR
AU  - V. N. Kuznetsov
AU  - O. A. Matveeva
TI  - Analogue of the Duffin--Scheffer theorem for one class of Dirichlet series with finite-valued coefficients
JO  - Čebyševskij sbornik
PY  - 2018
SP  - 243
EP  - 251
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2018_19_4_a12/
LA  - ru
ID  - CHEB_2018_19_4_a12
ER  - 
%0 Journal Article
%A V. N. Kuznetsov
%A O. A. Matveeva
%T Analogue of the Duffin--Scheffer theorem for one class of Dirichlet series with finite-valued coefficients
%J Čebyševskij sbornik
%D 2018
%P 243-251
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2018_19_4_a12/
%G ru
%F CHEB_2018_19_4_a12
V. N. Kuznetsov; O. A. Matveeva. Analogue of the Duffin--Scheffer theorem for one class of Dirichlet series with finite-valued coefficients. Čebyševskij sbornik, Tome 19 (2018) no. 4, pp. 243-251. http://geodesic.mathdoc.fr/item/CHEB_2018_19_4_a12/

[1] L. Biberbakh, Analiticheskoe prodolzhenie, Nauka, M., 1970

[2] O. A. Matveeva, “Approksimatsionnye polinomy i povedenie L-funktsii Dirikhle v kriticheskoi polose”, Izvestiya Sarat. un-ta. Matematika, Mekhanika. Informatika, 2013, no. 4-2, 80–84

[3] O. A. Matveeva, Analiticheskie svoistva opredelennykh klassov ryadov Dirikhle i nekotorye zadachi teorii L-funktsii Dirikhle, Dissertatsiya na soiskanie uchebnoi stepeni k.f.-m.n. po spetsialnosti 01.01.06, Ulyanovsk, 2014

[4] V. N. Kuznetsov, O. A. Matveeva, “O granichnom povedenii odnogo klassa ryadov Dirikhle s multiplikativnymi koeffitsientami”, Chebyshevskii sbornik, 17:2 (2016), 142–149

[5] V. N. Kuznetsov, O. A. Matveeva, “Approksimatsionnye polinomy Dirikhle i nekotorye svoistva L-funktsii Dirikhle”, Chebyshevskii sbornik, 18:4 (2017), 196–204

[6] V. N. Kuznetsov, O. A. Matveeva, “O granichnom povedenii odnogo klassa ryadov Dirikhle s multiplikativnymi koeffitsientami”, Chebyshevskii sbornik, 17:3 (2016), 115–124

[7] V. N. Kuznetsov, O. A. Matveeva, “K zadache analiticheskogo prodolzheniya ryadov Dirikhle s konechnoznachnymi koeffitsientam kak tselykh funktsii na kompleksnuyu ploskost”, Chebyshevskii sbornik, 18:4 (2017), 205–2013

[8] V. N. Kuznetsov, O. A. Matveeva, “Granichnoe povedenie i zadacha analiticheskogo prodolzheniya odnogo klassa ryadov Dirikhle s multiplikativnymi koeffitsientami”, Chebyshevskii sbornik, 19:2 (2018)

[9] V. N. Kuznetsov, O. A. Matveeva, “K odnoi zadache Yu. V. Linnika”, Chebyshevskii sbornik, 19:3 (2018) | MR

[10] V. N. Kuznetsov, O. A. Matveeva, “K probleme obobschennykh kharakterov”, Chebyshevskii sbornik, 19:3 (2018) | MR

[11] A. Gurvits, R. Kurant, Teoriya funktsii, Nauka, M., 1968

[12] A. N. Markushevich, Teoriya analiticheskikh funktsii, v. 2, Nauka, M., 1967 | MR

[13] V. N. Kuznetsov, “Analog teoremy Sege dlya odnogo klassa ryadov Dirikhle”, Mat. zametki, 36:6 (1984), 805–813 | MR | Zbl

[14] N. G. Chudakov, Yu. V. Linnik, “Ob odnom klasse vpolne multiplikativnykh funktsii”, DAN SSSR, 74:2 (1950), 133–136

[15] N. G. Chudakov, “Obobschennye kharaktery”, Mezhdunar. kongress matematikov v Nitstse-1970, Doklady sovetskikh matematikov, Nauka, M., 1972, 335