| Abstract: | For the Dirichlet series F(s) = ?n = 1￥ anexp{ sln } F(s) = \sum\nolimits_{n = 1}^\infty {{a_n}\exp \left\{ {s{\lambda_n}} \right\}} with abscissa of absolute convergence σ
a
=0, we establish conditions for (λ
n
) and (a
n
) under which lnM( s, F ) = TR( 1 + o(1) )exp{ rR | / |
| s| } \ln M\left( {\sigma, F} \right) = {T_R}\left( {1 + o(1)} \right)\exp \left\{ {{{{{\varrho_R}}} \left/ {{\left| \sigma \right|}} \right.}} \right\} for σ ↑ 0, where
M( s, F ) = sup{ | F( s+ it ) |:t ? \mathbbR } M\left( {\sigma, F} \right) = \sup \left\{ {\left| {F\left( {\sigma + it} \right)} \right|:t \in \mathbb{R}} \right\} and T
R
and ϱ
R
are positive constants. |
