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, Tome 8 (1996) no. 2, pp. 315-329

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

∑ m≤T d κ T (m) m σ T +it
where d κ T (m) denote the coefficients of the Dirichlet series expansion of the function ζ κ T (s) in the half-plane σ>1 κ T =(2 -1 logl T ) -1 2 , σ T =1 2+1n 2 l T l T and l T >0, l T ≤ 1n T and l T →∞ as T→∞, is proved.

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

∑ m≤T d κ T (m) m σ T +it
où d κ T (m) sont les coefficients du développement en série de Dirichlet de la fonction ζ κ T (s) dans le demi-plan σ>1, κ T =(2 -1 logl T ) -1 2 , σ T =1 2+log 2 l T l T , l T >0, l T ≤logT et l T →∞ lorsque T→∞.

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     author = {Antanas Laurin\v{c}ikas},
     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},
     year = {1996},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     zbl = {0871.11059},
     mrnumber = {1438472},
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Antanas Laurinčikas. 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, Tome 8 (1996) no. 2, pp. 315-329. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_315_0/

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