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Consider a function $f(x_1,\ldots,x_n)$ of $n$ complex variables. Define $$f_{\mathrm{symm}}(x_1,\ldots,x_n) = 2^{-n}\sum_{\varepsilon_1,\ldots,\varepsilon_n=\pm 1} f(\varepsilon_1x_1,\ldots,\...

There exist a "standard" or canonical way to construct a real valued function whose Mellin transform has a prescribed set of zeroes? Clearly for some set of zeroes this could be impossible ...