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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 554–564 (Mi msb3326)  

On an estimate for a Dirichlet polynomial and some of its applications

A. F. Leont'ev


Abstract: Let $L(\mu)$ be an entire function of exponential type and of completely regular growth, $\overline D$ its conjugate diagram, and $\overline D(\alpha)$ the displacement of $\overline D$ by the vector $\alpha$. Next let $\alpha_1$ and $\alpha_2$ be arbitrary fixed points, and $D_1$ and $D_2$ be regions such that $D_1\supset\overline D(\alpha_1)$ and $D_2\supset\overline D(\alpha_2)$. The estimate
$$ |P(z)|\leqslant N\max(M_1,M_2),\qquad M_j=\max_{t\in\overline D_j}|P(t)|\quad(j=1,2), $$
where $N$ does not depend on $P(z)$, is established for a Dirichlet polynomial $P(z)$, whose exponents are the zeros of $L(\mu)$, in some region $G$ containing the set $\overline D(\alpha)$, $\alpha\in[\alpha_1,\alpha_2]$. A number of corollaries follow from the estimate.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 575–586

Bibliographic databases:

UDC: 517.53
MSC: Primary 30A04, 30A06, 30A64; Secondary 30A16
Received: 15.01.1973

Citation: A. F. Leont'ev, “On an estimate for a Dirichlet polynomial and some of its applications”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 554–564; Math. USSR-Sb., 20:4 (1973), 575–586

Citation in format AMSBIB
\Bibitem{Leo73}
\by A.~F.~Leont'ev
\paper On~an estimate for a~Dirichlet polynomial and some of its applications
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 4(8)
\pages 554--564
\mathnet{http://mi.mathnet.ru/msb3326}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=328089}
\zmath{https://zbmath.org/?q=an:0278.30007}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 4
\pages 575--586
\crossref{https://doi.org/10.1070/SM1973v020n04ABEH001997}


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