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This article is cited in 3 scientific papers (total in 3 papers)
Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients
V. N. Kuznetsov, O. A. Matveeva Saratov State University
Abstract:
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.
Received: 20.09.2016 Accepted: 12.12.2016
Citation:
V. N. Kuznetsov, O. A. Matveeva, “Approximation approach in certain problems of the theory of Dirichlet series with multiplicative coefficients”, Chebyshevskii Sb., 17:4 (2016), 124–131
Linking options:
https://www.mathnet.ru/eng/cheb520 https://www.mathnet.ru/eng/cheb/v17/i4/p124
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Abstract page: | 176 | Full-text PDF : | 45 | References: | 34 |
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