Abstract: | We establish the relation between the increase of the quantityM(σ,F) = ∣a
0∣ + ∑
n=1
∞
∣a
n
∣ exp (σλ
n
) and the behavior of sequences (|a
n
|) and (λ
n
), where (λ
n
) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a
0 + ∑
n=1
∞
a
n
e
sλn
,s=σ+it, is the Dirichlet entire series.
Lviv University, Lviv. Translated from Ukrainskii Matematicheskii Zhurmal, Vol. 51, No. 8, pp. 1149–1153, August, 1999. |