Article

    Ufa Mathematical Journal
    Volume 7, Number 4, pp. 15-23

    Exactness of estimates for $k$-\lowercase{th} order of Dirichlet series in a semi-strip


    Aitkuzhina N.N., Gaisin A.M.

    DOI:10.13108/2015-7-4-15

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    We study Dirichlet series converging only in a half-plane such that their sequence of exponents admits an extension to a ``regular'' sequence. We prove the exactness of two-sided estimates for $k$-order of the sum of the Dirichlet series in a semi-strip whose width depends on the special distribution density of the exponents.