On the zeros of a class of generalised Dirichlet series-XI

Balasubramanian, R. ; Ramachandra, K. (1992) On the zeros of a class of generalised Dirichlet series-XI Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 102 (3). pp. 225-233. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/102/3/225-2...

Related URL: http://dx.doi.org/10.1007/BF02837859

Abstract

A sufficiently large class of generalised Dirichlet series is shown to have lots of zeros inσ > 1/2. Some examples are (i)ξ'(s)-a (a any complex constant) (ii) α -ζ(s)-∑n=0 ((n+√2)−2−(n+1)−1) (where α is any positive constant) and (iii) σ+∑ n=1 (−1) n (logn)λ n −s (where λ is any real constant > 1/2 and α any complex constant). Here as is usual we have writtens = σ + it.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Zeros; Generalised Dirichlet Series; Riemann Zeta-function
ID Code:1352
Deposited On:05 Oct 2010 12:42
Last Modified:16 May 2016 12:29

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