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pro vyhledávání: '"30B20, 30D20"'
We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erd\H{o}s and R\'enyi and recent results of Kuryliak and Skaskiv. Our results are then applied
Externí odkaz:
http://arxiv.org/abs/2409.04235
Let $F$ be an entire function represented by absolutely convergent for all $z\in\mathbb{C}$ Dirichlet series of the form $ F(z) = \sum\nolimits_{n=0}^{+\infty} a_{n}e^{z\lambda_{n}},$\ where a sequence $(\lambda_n)$ such that $\lambda_n\in\mathbb{R}\
Externí odkaz:
http://arxiv.org/abs/1512.08032
For entire functions $f(z)=\sum_{n=0}^{+\infty}a_nz^n, z\in {\Bbb C},$ P. L${\rm \acute{e}}$vy (1929) established that in the classical Wiman's inequality $M_f(r)\leq\mu_f(r)\times $ $\times(\ln\mu_f(r))^{1/2+\varepsilon},\ \varepsilon>0,$ which hold
Externí odkaz:
http://arxiv.org/abs/1307.6164
Let $F$ be an entire function represented by absolutely convergent for all $z\in\mathbb{C}$ Dirichlet series of the form $ F(z) = \sum\nolimits_{n=0}^{+\infty} a_{n}e^{z\lambda_{n}},$\ where a sequence $(\lambda_n)$ such that $\lambda_n\in\mathbb{R}\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5b871323b407b800b79f4c72f8a1590