For L-functions with multiple Gamma factors, the functional equation holds if and only if the coefficients satisfy Voronoi-type summation identities.
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Equivalence between the Functional Equation and Vorono\"{\i}-type summation identities for a class of $L$-Functions
For L-functions with multiple Gamma factors, the functional equation holds if and only if the coefficients satisfy Voronoi-type summation identities.