Sequences of maximal terms and central exponents of derivatives of Dirichlet series (Q1280695)

Let \(F(s)=\sum_{n=1}^\infty a_{n}\exp(s\lambda_{n})\), \(\text{Re }s<A\), where \(0<\lambda_{n}\nearrow+\infty\), \(A\in(-\infty,+\infty]\), and \(a_{n}\neq 0\) for any \(n\). For \(\sigma\in(-\infty,A)\) define \(\mu(\sigma,F):=\max\{| a_{n}| \exp(\sigma\lambda_{n})\: n\in\mathbb N\}\), \(\nu(\sigma,F):=\max\{n\in\mathbb N\:| a_{n}| \exp(\sigma\lambda_{n})= \mu(\sigma,F)\}=\) the central index, \(\Lambda(\sigma,F):=\lambda_{\nu(\sigma,F)}=\) the central exponent of the series. The author studies the asymptotic behavior of \(\mu(\sigma,F^{(m)})\) and \(\Lambda(\sigma,F^{(m)})\) when \(m\rightarrow+\infty\).