Geodesic
Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients
Čebyševskij sbornik, Tome 17 (2016) no. 4, pp. 124-131

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

In this paper we consider a class of Dirichlet series with multiplicative coefficients which define functions holomorphic in the right half of the complex plane, and for which there are sequences of Dirichlet polynomials that converge uniformly to these functions in any rectangle within the critical strip. We call such polynomials approximating Dirichlet polynomials. We study the properties of the approximating polynomials, in particular, for those Dirichlet series, whose coefficients are determined by nonprincipal generalized characters, i.e. finite-valued numerical characters which do not vanish on almost all prime numbers and whose summatory function is bounded. These developments are interesting in connection with the problem of the analytical continuation of such Dirichlet series to the entire complex plane, which in turn is tied with the solution of a well-known Chudakov hypothesis about every generalized character being a Dirichlet character. Bibliography: 15 items.
Keywords: Dirichlet series, summatory function of coeffiecients, generalized character, Dirichlet character, approximating polynomials. 
@article{CHEB_2016_17_4_a8,
     author = {V. N. Kuznetsov and O. A. Matveeva},
     title = {Approximation approach in certain problems of the theory of {Dirichlet} series with multiplicative coefficients},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {124--131},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2016_17_4_a8/}
}
TY  - JOUR
AU  - V. N. Kuznetsov
AU  - O. A. Matveeva
TI  - Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients
JO  - Čebyševskij sbornik
PY  - 2016
SP  - 124
EP  - 131
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2016_17_4_a8/
LA  - ru
ID  - CHEB_2016_17_4_a8
ER  - 
%0 Journal Article
%A V. N. Kuznetsov
%A O. A. Matveeva
%T Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients
%J Čebyševskij sbornik
%D 2016
%P 124-131
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2016_17_4_a8/
%G ru
%F CHEB_2016_17_4_a8
V. N. Kuznetsov; O. A. Matveeva. Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients. Čebyševskij sbornik, Tome 17 (2016) no. 4, pp. 124-131. http://geodesic.mathdoc.fr/item/CHEB_2016_17_4_a8/