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

mT 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

mT d κ T (m) m σ T +it
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.

@article{JTNB_1996__8_2_315_0,
     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},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
     zbl = {0871.11059},
     mrnumber = {1438472},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_315_0/}
}
TY  - JOUR
AU  - Antanas Laurinčikas
TI  - Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1996
SP  - 315
EP  - 329
VL  - 8
IS  - 2
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_315_0/
LA  - en
ID  - JTNB_1996__8_2_315_0
ER  - 
%0 Journal Article
%A Antanas Laurinčikas
%T Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
%J Journal de théorie des nombres de Bordeaux
%D 1996
%P 315-329
%V 8
%N 2
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_315_0/
%G en
%F JTNB_1996__8_2_315_0
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, Volume 8 (1996) no. 2, pp. 315-329. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_315_0/

[1] H. Bohr and B. Jessen, Über die Wertverteilung der Riemannschen Zeta funktion, Ernste Mitteilung, Acta Math. 51 (1930), 1-35. | JFM

[2] H. Bohr and B. Jessen, Über die Wertverteilung der Riemannschen Zeta funktion, Zweite Mitteilung, Acta Math. 58 (1932),1-55. | JFM | Zbl

[3] B. Jessen and A. Wintner, Distribution functions and the Riemann zeta-function, Trans.Amer.Math.Soc. 38 (1935), 48-88. | JFM | MR | Zbl

[4] V. Borchsenius and B. Jessen, Mean motions and values of the Riemann zeta-function, Acta Math. 80 (1948), 97-166. | MR | Zbl

[5] A. Laurinčikas, Limit theorems for the Riemann zeta-function on the complex space, Prob. Theory and Math. Stat., 2, Proceedings of the Fifth Vilnius Conference, VSP/Mokslas (1990), 59-69. | MR | Zbl

[7] A.P. Laurincikas, Distribution of values of complex-valued functions, Litovsk. Math. Sb. 15 Nr.2 (1975), 25-39, (in Russian); English transl. in Lithuanian Math. J., 15, 1975. | MR | Zbl

[8] D. Joyner, Distribution Theorems for L-functions, John Wiley (986). | Zbl

[9] A.P. Laurincikas, A limit theorem for the Riemann zeta-function close to the critical line. II, Mat. Sb., 180, 6 (1989), 733-+749, (in Russian); English transl. in Math. USSR Sbornik, 67, 1990. | MR | Zbl

[10] A. Laurincikas, A limit theorem for the Riemann zeta-function in the complex space, Acta Arith. 53 (1990), 421-432. | MR | Zbl

[11] D.R. Heath-Brown, Fractional moments of the Riemann zeta-function, J.London Math. Soc. 24(2) (1981), 65-78. | MR | Zbl

[12] A. Ivic, The Riemann zeta-function John Wiley, 1985. | MR | Zbl

[13] P. Billingsley, Convergence of Probability Measures, John Wiley, 1968. | MR | Zbl

[14] H. Heyer, Probability measures on locally compact groups, Springer-Verlag, Berlin-Heidelberg- New York (1977). | MR | Zbl

[15] H.L. Montgomery and R.C. Vaughan, Hilbert's inequality, J. London Math. Soc. 8(2) (1974), 73-82. | MR | Zbl