Geodesic
Sequences of maximal terms and central exponents of derivatives of Dirichlet series
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 457-467.

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For the Dirichlet series corresponding to a function $F$ with positive exponents increasing to $\infty$ and with abscissa of absolute convergence $A\in(-\infty,+\infty]$, it is proved that the sequences $\bigl(\mu(\sigma,F^{(m)})\bigr)$ of maximal terms and $\bigl(\Lambda(\sigma,F^{(m)})\bigr)$ of central exponents are nondecreasing to $\infty$ as $m\to\infty$ for any given $\sigma$, and $$ \varlimsup_{m\to\infty}\frac{\ln\mu(\sigma,F^{(m)})}{m\ln m}\le1 \quad\text{and}\quad \varlimsup_{m\to\infty}\frac{\ln\Lambda(\sigma,F^{(m)})}{\ln m}\le1. $$ Necessary and sufficient conditions for putting the equality sign and replacing $\varlimsup$ by $\lim$ in these relations are given. 
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     author = {M. N. Sheremeta},
     title = {Sequences of maximal terms and central exponents of derivatives of {Dirichlet} series},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a17/}
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M. N. Sheremeta. Sequences of maximal terms and central exponents of derivatives of Dirichlet series. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 457-467. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a17/

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