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On the lower order ( R ) of an entire Dirichlet series

P. K. Jain, D. R. Jain (1974)

Annales de l'institut Fourier

The estimations of lower order ( R ) λ in terms of the sequences { a n } and { λ n } for an entire Dirichlet series f ( s ) = n = 1 a n e s λ n , have been obtained, namely : λ = max { λ n p } lim inf p λ n p log λ n p - 1 log | a n p | - 1 = max { λ n p } lim inf p ( λ n p - λ n p - 1 ) log λ n p - 1 log | a n p - 1 | a n p | . One of these estimations improves considerably the estimations earlier obtained by Rahman (Quart. J. Math. Oxford, (2), 7, 96-99 (1956)) and Juneja and Singh (Math. Ann., 184(1969), 25-29 ).

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