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In 2001, M.Rekos described the analytic behavior for a function $f(z)$connected with the Euler totient function for Im$z > 0$ (see (1.2)) imitatingthe previous research of [1] and [3]. In the present paper, for Im$z > 0$ wedescribe the analytic behavior of the generalized function $f(z,F)$ (see(2.1)), where the function $F$ belongs to the subclass of the Selberg classwhich has a polynomial Euler product and satisfies some special conditions.

On some analytic properties of a function associated with the Selberg class satisfying certain special conditions