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Under the condition that $F_{\\beta}(z)$ has no zeros in $D(0,r)$, the scaled zero counting measure converges to a limiting measure $\\mu_{0}^{\\beta}$ vaguely in distribution. This limit exhibits a \\emph{forbidden region} \\[ \\bigl\\{1<|z|<e^{1/\\beta}\\bigr\\}, \\] which zeros asymptotically avoid. 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Under the condition that $F_{\\beta}(z)$ has no zeros in $D(0,r)$, the scaled zero counting measure converges to a limiting measure $\\mu_{0}^{\\beta}$ vaguely in distribution. This limit exhibits a \\emph{forbidden region} \\[ \\bigl\\{1<|z|<e^{1/\\beta}\\bigr\\}, \\] which zeros asymptotically avoid. 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