Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 315-329.

A limit theorem in the space of continuous functions for the Dirichlet polynomial

 $\sum _{m\le T}\frac{{d}_{{\kappa }_{T}}\left(m\right)}{{m}^{{\sigma }_{T}+it}}$
where ${d}_{{\kappa }_{T}}\left(m\right)$ denote the coefficients of the Dirichlet series expansion of the function ${\zeta }^{{\kappa }_{T}}\left(s\right)$ in the half-plane $\sigma >1$ ${\kappa }_{T}={\left({2}^{-1}log{l}_{T}\right)}^{-\frac{1}{2}}$, ${\sigma }_{T}=\frac{1}{2}+\frac{1{n}^{2}{l}_{T}}{{l}_{T}}$ and ${l}_{T}>0$, ${l}_{T}\le$ 1n $T$ and ${l}_{T}\to \infty$ as $T\to \infty$, is proved.

Dans cet article on prouve un théorème limite dans l’espace des fonctions continues pour le polynôme de Dirichlet

 $\sum _{m\le T}\frac{{d}_{{\kappa }_{T}}\left(m\right)}{{m}^{{\sigma }_{T}+it}}$
${d}_{{\kappa }_{T}}\left(m\right)$ sont les coefficients du développement en série de Dirichlet de la fonction ${\zeta }^{{\kappa }_{T}}\left(s\right)$ dans le demi-plan $\sigma >1$, ${\kappa }_{T}={\left({2}^{-1}log{l}_{T}\right)}^{-\frac{1}{2}}$, ${\sigma }_{T}=\frac{1}{2}+\frac{{log}^{2}{l}_{T}}{{l}_{T}}$, ${l}_{T}>0$, ${l}_{T}\le logT$ et ${l}_{T}\to \infty$ lorsque $T\to \infty .$

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author = {Laurin\v{c}ikas, Antanas},
title = {Limit theorem in the space of continuous functions for the {Dirichlet} polynomial related with the {Riemann} zeta-funtion},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {315--329},
publisher = {Universit\'e Bordeaux I},
volume = {8},
number = {2},
year = {1996},
mrnumber = {1438472},
zbl = {0871.11059},
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Laurinčikas, Antanas. Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 315-329. http://archive.numdam.org/item/JTNB_1996__8_2_315_0/

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