Functional equation of a special Dirichlet series

Ibrahim A. Abou-Tair

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-9

Abstract:

In this paper we study the special Dirichlet series L ( s ) = 2 3 ∑ n = 1 ∞ sin ( 2 π n 3 ) n − s , s ∈ C This series converges uniformly in the half-plane Re ( s ) > 1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The values of the function L at the points 0 , ± 1 , − 2 , ± 3 , − 4 , ± 5 , … are obtained. The values at the positive integers 1 , 3 , 5 , … are determined by means of a functional equation satisfied by L .

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:308272

DOI: 10.1155/S0161171287000462

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