Geodesic
Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves
Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 37-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve. 
@article{MZM_2005_78_1_a3,
     author = {A. M. Gaisin and I. D. Latypov},
     title = {Asymptotic {Behavior} of the {Sum} of the {Dirichlet} {Series} of {Prescribed} {Growth} on {Curves}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {37--51},
     year = {2005},
     volume = {78},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a3/}
}
TY  - JOUR
AU  - A. M. Gaisin
AU  - I. D. Latypov
TI  - Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves
JO  - Matematičeskie zametki
PY  - 2005
SP  - 37
EP  - 51
VL  - 78
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a3/
LA  - ru
ID  - MZM_2005_78_1_a3
ER  - 
%0 Journal Article
%A A. M. Gaisin
%A I. D. Latypov
%T Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves
%J Matematičeskie zametki
%D 2005
%P 37-51
%V 78
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a3/
%G ru
%F MZM_2005_78_1_a3
A. M. Gaisin; I. D. Latypov. Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves. Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 37-51. http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a3/

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

[2] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[3] Gaisin A. M., “Otsenka rosta i ubyvaniya tseloi funktsii beskonechnogo poryadka na krivykh”, Matem. sb., 194:8 (2003), 55–82 | MR

[4] Beurling A., “Some theorems on boundedness of analytic functions”, Duke Math. J., 16 (1949), 355–359 | DOI | MR | Zbl

[5] Goldberg A. A., Ostrovskii I. V., Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR

[6] Gaisin A. M., Latypov I. D., “Asimptotika logarifma maksimalnogo chlena izmenennogo ryada Dirikhle”, Izv. vuzov. Matem., 2002, no. 9 (484), 15–24 | MR | Zbl

[7] Pólya. G., “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, Math. Z., 29 (1929), 549–640 | DOI | MR

[8] Sheremeta M. N., “O roste na deistvitelnoi osi tseloi funktsii, predstavlennoi ryadom Dirikhle”, Matem. zametki, 33:2 (1983), 235–245 | MR | Zbl

[9] Gaisin A. M., “Povedenie summy ryada Dirikhle zadannogo rosta”, Matem. zametki, 50:4 (1991), 47–56 | MR | Zbl

[10] Gaisin A. M., “Ob odnoi gipoteze Polia”, Izv. RAN. Ser. matem., 58:2 (1994), 73–92 | Zbl

[11] Kheiman U., Meromorfnye funktsii, Mir, M., 1966