Abstract:
In this paper we study the analytic properties of Dirichlet L -functions in the critical strip,
characteristic for almost periodic functions. The research is based on
Approximation approach, consisting in the construction of Dirichlet polynomials,
which are almost periodic functions, "rapidly convergent"
in the critical strip to Dirichlet L -functions.
On this path, for any
rectangle lying in the critical strip, the existence of
ε -almost period for the Dirichlet L-function, we obtain the estimate
constants of uniform continuity. Issues related to
studying other properties of Dirichlet L -functions are discussed.
Keywords:
Dirichlet approximation polynomials, Dirichlet L-functions, almost periodic functions.
Citation:
O. A. Matveeva, V. N. Kuznetsov, “On Dirichlet approximation polynomials and some properties of Dirichlet L-functions”, Chebyshevskii Sb., 18:4 (2017), 297–305
\Bibitem{MatKuz17}
\by O.~A.~Matveeva, V.~N.~Kuznetsov
\paper On Dirichlet approximation polynomials and some properties of Dirichlet $L$-functions
\jour Chebyshevskii Sb.
\yr 2017
\vol 18
\issue 4
\pages 297--305
\mathnet{http://mi.mathnet.ru/cheb613}
\crossref{https://doi.org/10.22405/2226-8383-2017-18-4-296-304}
Linking options:
https://www.mathnet.ru/eng/cheb613
https://www.mathnet.ru/eng/cheb/v18/i4/p297
This publication is cited in the following 1 articles:
V. N. Kuznetsov, O. A. Matveeva, “Analogue of the Duffin–Scheffer theorem for one class of Dirichlet series with finite-valued coefficients”, Chebyshevskii Sb., 19:4 (2018), 243–251
Citation in format AMSBIB
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