I am new to the Riemann zeta function.
In the beginning of section 2 of Bruce c. Berndt, the number of zeros for $\zeta^{(k)}(s)$, J. London Math. Soc. (2), Vol 2, 1970, p. 577-580, the author made the following claim:
From the general theory of Dirichlet series, $\zeta^{(k)}(s)$ has a right half-plane free of zeros.
Could someone kindly elaborate on the above claim and point out which result from the "general theory of Dirichlet series" that the author was using please?