Are there are other known functions that give the same set of zeros as the Riemann zeta function inside the critical strip besides $\eta(s)$?

Question

The zeros of the Dirichlet's eta function $\eta(s)$ inside the critical strip match the non-trivial zeros of the Riemann zeta function $\zeta(s)$, as $\eta(s) = (1 - 2^{1-s}) \zeta(s)$.

What are the other known functions that give the same set of zeros of $\zeta(s)$ inside the critical strip?

EDIT:

I'm interested in functions given explicitly in series form:

$$\sum_{n = 1}^{\infty} f(n) \, n^{-s}$$