论文标题
傅立叶系数的欧拉尔体性形式的傅立叶系数
Eulerianity of Fourier coefficients of automorphic forms
论文作者
论文摘要
我们研究了自态形式的傅立叶系数的欧拉尔特性问题（因素方差），我们证明了一种一般的转移定理，该定理允许一个人从另一个系数中推断出某些系数的欧拉尔斯。我们还建立了傅立叶系数的“隐藏”不变性属性。我们将这些结果应用于最小和最小的自动形态表示，并针对大型傅立叶和傅里叶 - 雅各比系数推断出Eulerianity。特别是，我们证明了抛物线傅立叶系数的欧拉尔特性，具有最小的Eisenstein系列的特征，以最小值和近代的ADE型类型组的最小和最小表示，这是字符串理论中感兴趣的。
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.
