Return to Revisions

An example which is almost trivial: take the sequence $\{1,4,8,16,32\ldots\}$, i.e. powers of $2$ omitting two itself. For real part of $s>0$, the Dirichlet series is a convergent geometric series, summing as $$ \frac{1-2^s+4^s}{1-2^s} $$ which has a meromorphic continuation. The zeros are all purely imaginary, at $$ \frac{\pi i(6n\pm1)}{3\log(2)},\qquad \text{integer } n $$ if I've done the calculation correctly.