We study the uniqueness of functions in the extended Selberg class. It was shown in Ki (Adv Math 231, 2484–2490, 2012) that if for a nonzero complex number the inverse images L1-1 and L2-1(c)of two functions satisfying the same functional equation in the extended Selberg class are the same, then L1(s) and L 2(s) are identical. Here we prove that this holds even without the assumption that they satisfy the same functional equation.
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