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

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.