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 Chebyshevskii Sb., 2017, Volume 18, Issue 4, Pages 297–305 (Mi cheb613)

On Dirichlet approximation polynomials and some properties of Dirichlet $L$-functions

O. A. Matveeva, V. N. Kuznetsov

Saratov State University

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 $\varepsilon$ -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.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00399_à

DOI: https://doi.org/10.22405/2226-8383-2017-18-4-296-304

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UDC: 511.3
Accepted:14.12.2017

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

Citation in format AMSBIB
\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}