Abstract:We 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.

---

中文翻译：

---

自守形式的傅立叶系数的欧拉性

摘要：我们研究了自守形式傅里叶系数的欧拉性（可分解性）问题，并证明了一个通用的传递定理，它允许人们从另一个系数的欧拉性推导出某些系数的欧拉性。我们还建立了傅立叶系数的“隐藏”不变性。我们将这些结果应用于极小和次极小自守表示，并推导出一大类傅立叶和傅立叶-雅可比系数的欧拉性。特别是，我们在弦理论中感兴趣的 ADE 类型群的最小和次最小表示中证明了具有最大秩特征的抛物线傅立叶系数的欧拉性。

---