Geodesic
Asymptotic estimate of the sum of a Dirichlet series on curves
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 810-816.

Voir la notice de l'article provenant de la source Math-Net.Ru

Under quite general conditions, we obtain an asymptotic estimate of the sum of an entire Dirichlet series on curves. The result generalizes the well-known Pavlov and Kövari theorems 
@article{MZM_1997_61_6_a1,
     author = {A. M. Gaisin},
     title = {Asymptotic estimate of the sum of a {Dirichlet} series on curves},
     journal = {Matemati\v{c}eskie zametki},
     pages = {810--816},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a1/}
}
TY  - JOUR
AU  - A. M. Gaisin
TI  - Asymptotic estimate of the sum of a Dirichlet series on curves
JO  - Matematičeskie zametki
PY  - 1997
SP  - 810
EP  - 816
VL  - 61
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a1/
LA  - ru
ID  - MZM_1997_61_6_a1
ER  - 
%0 Journal Article
%A A. M. Gaisin
%T Asymptotic estimate of the sum of a Dirichlet series on curves
%J Matematičeskie zametki
%D 1997
%P 810-816
%V 61
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a1/
%G ru
%F MZM_1997_61_6_a1
A. M. Gaisin. Asymptotic estimate of the sum of a Dirichlet series on curves. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 810-816. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a1/

[1] Pavlov A. I., “O roste po krivym tselykh funktsii, zadannykh lakunarnymi stepennymi ryadami”, Sib. matem. zh., 13:5 (1972), 1169–1181 | MR | Zbl

[2] Kövari T., “On the asymptotic paths of entire functions with gap power series”, J. Anal. Math., 15 (1965), 281–286 | DOI | MR | Zbl

[3] Korevaar J., Dixon M., “Interpolation, strongly nonspanning powers and Macintyre exponents”, Indag. Math. (N. S.), 40:2 (1978), 243–258 | MR

[4] Gaisin A. M., “Asimptoticheskoe povedenie summy tselogo ryada Dirikhle na krivykh”, Issledovaniya po teorii priblizhenii, BNTs UrO AN SSSR, Ufa, 1989, 3–15 | MR | Zbl

[5] Berndtsson B., “A note on Pavlov–Korevaar–Dixon interpolation”, Nederl. Acad. Wet. Proc., 81 (1978), 400–414

[6] Murai T., “The deficiency of entire functions with Fejér gaps”, Ann. Inst. Fourier, 33:3 (1983), 39–58 | MR | Zbl

[7] Gaisin A. M., “Ob odnoi gipoteze Polia”, Izv. RAN. Ser. matem. (to appear)

[8] Krasichkov I. F., “Otsenka snizu dlya tselykh funktsii konechnogo poryadka”, Sib. matem. zh., 6:4 (1965), 840–861 | MR | Zbl

[9] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980

[10] Boichuk V. S., “O nekotorykh svoistvakh utochnennogo poryadka”, Sib. matem. zh., 20:2 (1979), 229–236 | MR

[11] Gaisin A. M., “Usilennaya nepolnota sistemy eksponent i problema Makintaira”, Matem. sb., 182:7 (1991), 931–945

[12] Macintyre A. J., “Asymptotic paths of integral functions with gap power series”, Proc. London Math. Soc., 2:3 (1952), 286–296 | DOI | MR | Zbl