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

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→∞.

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.

@article{JTNB_1996__8_2_315_0,
     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},
     doi = {10.5802/jtnb.171},
     zbl = {0871.11059},
     mrnumber = {1438472},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.171/}
}
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. doi : 10.5802/jtnb.171. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.171/

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