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Certain results on entire functions defined by bicomplex Dirichlet series

Jogendra Kumar

Abstract


In this work, we have introduced and studied the Bicomplex version of Complex Dirichlet Series  . We have derived condition for which the sum function of the Bicomplex Dirichlet Series represents an entire function. The Entireness of sum and Hadamard product of two Entire Bicomplex Dirichlet Series are also discussed.


Keywords


Dirichlet Series, Entire Dirichlet Series, Riemann Zeta Function, Hadamard Product

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References


M.E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers, Springer International Publishing, (2015)

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Rajiv K. Srivastava,Certain Topological aspects of Bicomplex Space, Bull. Pure and Appl. Math., 2(2),(2008), 222–234.

G. H. Hardy and M. Riesz, The General Theory of Dirichlet Series, Cambridge Univ. Press (1915).

E. C. Titchmarsh, The Theory of functions, Oxford University press (1960).

S. Mandelbrojt, Dirichlet series: Principles and Methods, Dordrecht Holland (1969).


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