Asymptotics of the entire functions with $\upsilon$-density of zeros along the logarithmic spirals
Keyword(s):
Let $\upsilon$ be the growth function such that $r\upsilon'(r)/\upsilon (r) \to 0$ as $r \to +\infty$, $l_\varphi^c = \{z=te^{i(\varphi+c \ln t)}, 1 \leqslant t < +\infty\}$ be the logarithmic spiral, $f$ be the entire function of zero order. The asymptotics of $\ln f(re^{i(\theta +c \ln r)})$ along ordinary logarithmic spirals $l_\theta^c$ of the function $f$ with $\upsilon$-density of zeros along $l_\varphi^c$ outside the $C_0$-set is found. The inverse statement is true just in case zeros of $f$ are placed on the finite logarithmic spirals system $\Gamma_m = \bigcup_{j=0}^m l_{\theta_j}^c$.
Keyword(s):
1973 ◽
Vol 51
◽
pp. 123-130
◽
Keyword(s):
1995 ◽
Vol 138
◽
pp. 169-177
◽
2016 ◽
Vol 56
(3)
◽
pp. 763-776
◽
1995 ◽
Vol 118
(3)
◽
pp. 527-542
◽
Keyword(s):
2010 ◽
Vol 129-131
◽
pp. 235-240
◽
Keyword(s):
1988 ◽
Vol 38
(3)
◽
pp. 351-356
◽
Keyword(s):
1966 ◽
Vol 15
(2)
◽
pp. 121-123
◽