具有单调系数和对数h-测度的整狄利克雷级数
Entire Dirichlet series with monotonous coefficients and logarithmic h-measure
摘要：
设$F$是一个整函数，对所有形式为$ F(z) = \sum\nolimits_{n=0}^{+\infty} a_{n}e^{zλ_{n}},$ \的$z\in\mathbb{C}$狄利克雷级数都是绝对收敛的，其中序列$(λ_n)$使得对任何$n\not=k$和$(\forall n\geq 0):\ 0\leqλ_n<β:=\sup\{λ_j:\ j\geq0\}\leq +\infty.$都是$λ_n\in\mathbb{R}\ \ (n\geq0)$，$λ_n\not=λ_k$ {设$h$是$[0,+\infty)$上的非减正连续函数，$Φ$是$[0,+\infty)$上的增正连续函数.}本文找到了$(μ_n)$和$(λ_n)$的条件，使得关系$F(x+iy)=(1+o(1))a_{ν(x, F)}e^{(x+iy)λ_{ν(x, F)}} $在$y\in\mathbb{R}$中一致地在有限对数$h$ -测度的某个集合$E$之外成立.
英文摘要：
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^{zλ_{n}},$\ where a sequence $(λ_n)$ such that $λ_n\in\mathbb{R}\ \ (n\geq0)$, $λ_n\not=λ_k$ for any $n\not=k$ and $(\forall n\geq 0):\ 0\leqλ_n<β:=\sup\{λ_j:\ j\geq0\}\leq +\infty.$ {Let $h$ be non-decrease positive continuous function on $[0,+\infty)$ and $Φ$ increase positive continuous on $[0,+\infty)$ function.} In this paper we {find} the condition {on} $(μ_n)$ and $(λ_n)$ {such that} the relation $F(x+iy)=(1+o(1))a_{ν(x, F)}e^{(x+iy)λ_{ν(x, F)}} $ holds as $x\to +\infty$\ outside some set $E$ of finite logarithmic $h$-measure uniformly in $y\in\mathbb{R}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
