The Nevanlinna characteristic and maximum modulus of entire functions of finite order with random zeros (in Ukrainian)
Let (r_n) be a positive nondecreasing sequence of finite genus tending to +∞ , and (η_n(ω)) be a sequence of independent random variables such that η_n(ω) are uniformly distributed on the circles |z|=r_n. Then for almost all ω the following assertion holds: if f is an entire function of finite...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2011-07-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/texts/2011/36_1/40-50.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let (r_n) be a positive nondecreasing sequence of finite genus tending to +∞ , and (η_n(ω)) be a sequence of independent random variables such that η_n(ω) are uniformly distributed on the circles |z|=r_n. Then for almost all ω the following assertion holds: if f is an entire function of finite order with zeros at the points η_n(ω) and only at them, then for every ε>0 we have ln M_f(r)=o(T^3/2_f(r)ln^{3+ε}T_f(r)), r→+∞, where M_f(r) is the maximum modulus and T_f(r) is the Nevanlinna characteristic of the function f. |
|---|---|
| ISSN: | 1027-4634 |