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In this note we investigate the existence of zeros of linear twists of$L$-functions outside of the critical strip. In particular, we show that theLerch zeta function $L(\lambda,\alpha,s)$ has infinitely many zeros for$1<\sigma<1+\eta$, for any $\eta>0$, when $\lambda$ is irrational and $\alpha$is rational. This settles the question on the existence of zeros of the Lerchzeta functions for $\sigma>1$.

Zeros of linear twists of $L$-functions outside the critical strip