Geodesic
Growth of entire functions represented by Dirichlet series
Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1545-1560 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let, $\displaystyle F(z)=\sum _{n=1}^\infty a_ne^{\lambda _nz}$ be an entire function represented in the whole of the plane by an absolutely convergent Dirichlet series such that $$ 0\leqslant \lambda _1<\lambda _2<\dotsb ,\qquad \varlimsup _{n\to \infty }\frac {\ln n}{\lambda _n}=\mu \in [0,+\infty ). $$ The connection between the growth of the quantity $$ M(F;x)=\sup \bigl \{|F(x+iy)|:|y|<+\infty \bigr \},\qquad x\to +\infty. $$ End the behaviour of $|a_n|$ and $\lambda_n$ as $n\to \infty$ is described in general form. 
@article{SM_1996_187_10_a6,
     author = {V. A. Oskolkov and L. I. Kalinichenko},
     title = {Growth of entire functions represented by {Dirichlet} series},
     journal = {Sbornik. Mathematics},
     pages = {1545--1560},
     year = {1996},
     volume = {187},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/}
}
TY  - JOUR
AU  - V. A. Oskolkov
AU  - L. I. Kalinichenko
TI  - Growth of entire functions represented by Dirichlet series
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 1545
EP  - 1560
VL  - 187
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/
LA  - en
ID  - SM_1996_187_10_a6
ER  - 
%0 Journal Article
%A V. A. Oskolkov
%A L. I. Kalinichenko
%T Growth of entire functions represented by Dirichlet series
%J Sbornik. Mathematics
%D 1996
%P 1545-1560
%V 187
%N 10
%U http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/
%G en
%F SM_1996_187_10_a6
V. A. Oskolkov; L. I. Kalinichenko. Growth of entire functions represented by Dirichlet series. Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1545-1560. http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/

[1] Ritt J. F., “On certain points in the theory of Dirichlet Series”, Amer. J. Math., 50:1 (1928), 73–86 | DOI | MR | Zbl

[2] Sugimura K., “Übertragung einiger Satze uas der Theorie der ganzen Funktionen auf Dirichletschen Reihen”, Math. Z., 29 (1929), 264–277 | DOI | MR

[3] Azpeitia A. G., “A remark on the Ritt order of entire functions defined by Dirichlet series”, Proc. Amer. Math. Soc., 12 (1961), 722–723 | DOI | MR | Zbl

[4] Azpeitia A. G., “On the Ritt order of entire Dirichlet series”, Quart. J. Math., 15:59 (1964), 275–277 | DOI | MR | Zbl

[5] Rahman Q. J., “On the lower order of entire functions defined by Dirichlet series”, Quart. J. Math., 7 (1956), 96–99 | DOI | MR | Zbl

[6] Reddy A. R., “On entire Dirichlet series of infinite order, I”, Rev. Mat. Iberoamericana, 27 (1967), 120–131 | MR | Zbl

[7] Reddy A. R., “On entire Dirichlet series of infinite order, II”, Rev. Mat. Iberoamericana, 29 (1969), 215–231 | MR | Zbl

[8] Orudzhev S. R., “O poryadke i tipe tselykh funktsii, predstavlennykh ryadami Dirikhle”, Izv. vuzov. Ser. matem., 1974, no. 7 (146), 60–65

[9] Pyanylo Ya. D., Sheremeta M. N., “O roste tselykh funktsii, predstavlennykh ryadami Dirikhle”, Izv. vuzov. Ser. matem., 1975, no. 10 (161), 91–93 | Zbl

[10] Sheremeta M. N., “O tselykh funktsiyakh, predstavlennykh ryadami Dirikhle”, Izv. vuzov. Ser. matem., 1978, no. 3 (190), 90–98 | Zbl

[11] Oskolkov V. A., “O roste tselykh funktsii, predstavlennykh regulyarno skhodyaschimisya funktsionalnymi ryadami”, Matem. sb., 100 (146):2 (6) (1976), 312–334 | MR | Zbl

[12] Oskolkov V. A., “O nekotorykh voprosakh teorii tselykh funktsii”, Matem. sb., 184:1 (1993), 129–148 | Zbl

[13] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR