Geodesic
On zeros of some analytic functions related to the Hurwitz zeta-function
Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 86-90.

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Let $\zeta(s,\alpha)$ denote the Hurwitz zeta-function. We prove that, for some classes of functions $F$, the function $F(\zeta(s,\alpha))$ has infinitely many zeros in the critical strip. 
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A. Laurinčikas; D. Šiaučiunas. On zeros of some analytic functions related to the Hurwitz zeta-function. Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 86-90. http://geodesic.mathdoc.fr/item/CHEB_2012_13_2_a11/

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