Journal ArticleEulerianity of Fourier coefficients of automorphic formsGourevitch, Dmitry; Gustafsson, Henrik; Kleinschmidt, Axel; Persson, Daniel; Sahi, SiddharthaWe study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden’ invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier–Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.2021-06-0710339420Representation Theory of the American Mathematical Society2516481 to 5071088-4165https://doi.org/10.1090/ert/5652001537; 1939600National Science Foundation