Balasubramanian, R. ; Ramachandra, K. (1994) On the zeros of a class of generalised Dirichlet series XIV Proceedings of the Indian Academy of Sciences  Mathematical Sciences, 104 (1). pp. 167176. ISSN 02534142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/104/1/1671...
Related URL: http://dx.doi.org/10.1007/BF02830880
Abstract
We prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.Theorem A.Let 0<θ <1/2 and let {a n }be a sequence of complex numbers satisfying the inequality ∑^{N}_{n=1}a^{n}(n+a^{n})^{s}=ζ(s)+∑^{∞}_{n=1}(a^{n}(n+a^{n})^{s}n^{s})in the rectangle ½δ≤ σ≤1/2+δ,T≤t≤2T)(where 0 <δ<1/2)is ≥C(θ,δ)T logT where C(θ,δ)is a positive constant independent of T provided T ≥T 0(θ,δ)a large positive constant. Theorem B.In the above theorem we can relax the condition on a n to and aN≤ (1/2θ)^{1}.Then the lower bound for the number of zeros in (σ≥ ½+δ,T≤t≤2T is O(T)provided for every ε > 0.
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Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Generalised Dirichlet Series; Distribution of Zeros; Neighbourhood of the Critical Line 
ID Code:  72431 
Deposited On:  29 Nov 2011 12:42 
Last Modified:  18 May 2016 17:41 
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