Geodesic
On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 253-259.

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

The following theorem is proved. Let $A(z)$ be an entire function of exponential type, and let its Borel transform $a(z)$ satisfy the following conditions: 1) $a(z)$ can be analytically continued to a certain Riemann surface $R$ with finite number of branch points, and it has only finitely many singularities $z_k$ on $R$; 2) in any plane with cuts by parallel rays issuing from the $z_k$, a branch of $z_k$ satisfies $$ \varlimsup_{z\to\infty}\frac{\ln|a(z)|}{|z|}\leq0. $$ Then $A(z)$ has completely regular growth. From this theorem it follows, in particular, that if $a(z)$ is an algebraic function or a single-valued function with a finite number of singularities, then $A(z)$ has completely regular growth. Bibliography: 6 titles. 
@article{IM2_1979_13_2_a2,
     author = {N. V. Govorov and N. M. Chernykh},
     title = {On the complete regularity of growth of the {Borel} transform of the analytic continuation of the associated function, which has a~finite number of singular points},
     journal = {Izvestiya. Mathematics },
     pages = {253--259},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a2/}
}
TY  - JOUR
AU  - N. V. Govorov
AU  - N. M. Chernykh
TI  - On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points
JO  - Izvestiya. Mathematics 
PY  - 1979
SP  - 253
EP  - 259
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a2/
LA  - en
ID  - IM2_1979_13_2_a2
ER  - 
%0 Journal Article
%A N. V. Govorov
%A N. M. Chernykh
%T On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points
%J Izvestiya. Mathematics 
%D 1979
%P 253-259
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a2/
%G en
%F IM2_1979_13_2_a2
N. V. Govorov; N. M. Chernykh. On the complete regularity of growth of the Borel transform of the analytic continuation of the associated function, which has a~finite number of singular points. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 253-259. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a2/

[1] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[2] Titchmarsh E., Teoriya funktsii, Gostekhizdat, M., 1951

[3] Govorov N. V., “Kraevaya zadacha Rimana s beskonechnym indeksom stepennogo poryadka menshe 1/2”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 6, Kharkov, 1968, 151–176 | MR | Zbl

[4] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1967 | MR

[5] Gurvits A., Kurant R., Teoriya funktsii, Nauka, M., 1968 | MR

[6] Evgrafov M. A., Analiticheskie funktsii, Nauka, M., 1968 | MR | Zbl