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On an entire function represented by multiple Dirichlet series

Lakshika Chutani (2021)

Mathematica Bohemica

Consider the space L of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space L the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained.

On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

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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