Automorphicity and mean-periodicity (Q520625)

It is known that the \(L\)-function corresponding to a smooth projective curve over a number field admits meromorphic continuation and satisfies the appropriate functional equation, if and only if a related function is mean-periodic in some space of functions; see [\textit{I. Fesenko} et al., Ann. Inst. Fourier 62, No. 5, 1819--1887 (2012; Zbl 1305.11079)]. The author studies the relationship between \(L\)-functions of this class and those arising as \(L\)-functions of automorphic representations. This is connected with results by \textit{M. Suzuki} [Prog. Math. 300, 339--361 (2012; Zbl 1277.11074)].