Eulerianity of Fourier coefficients of automorphic forms
Eulerianity of Fourier coefficients of automorphic forms
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DOI：
10.1090/ert/565
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发表时间：
2020-04
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影响因子：
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通讯作者：
D. Gourevitch;H. Gustafsson;A. Kleinschmidt;D. Persson;S. Sahi
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文献类型：
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作者：
D. Gourevitch;H. Gustafsson;A. Kleinschmidt;D. Persson;S. Sahi
我们研究的问题Eulerianity（factorizability）的傅立叶系数的自守形式，我们证明了一个一般的转移定理，允许一个推导的Eulerianity的某些系数从另一个系数。我们还建立了一个“隐藏”的不变性的傅立叶系数。我们将这些结果应用到最小和下一个最小的自守表示，并推导出一个大类的傅立叶和傅立叶-雅可比系数欧拉。特别是，我们证明了欧拉抛物傅立叶系数字符的最大秩一类爱森斯坦系列的最小和下一个最小的陈述群的ADE型，在弦理论的兴趣。
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.