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Q31Section II (Mathematics)31 of 180

Complex analysis — zeros of entire and analytic functions

Consider the statements: (i) An entire function with infinitely many zeros is identically zero. (ii) There exists an analytic function ff on the unit disk such that f(12n)=1n=f(12n+1)f\bigl(\frac1{2n}\bigr)=\frac1n=f\bigl(\frac1{2n+1}\bigr) for n=1,2,3,…n=1,2,3,\dots Then:

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