Algebraic twists of modular forms and Hecke orbits
Algebraic twists of modular forms and Hecke orbits
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DOI：
10.1007/s00039-015-0310-2
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发表时间：
2012-07
影响因子：
2.2
通讯作者：
É. Fouvry;E. Kowalski;P. Michel
中科院分区：
文献类型：
--
作者：
É. Fouvry;E. Kowalski;P. Michel
考虑了模形式的傅里叶系数与代数原点函数的相关问题。我们建立了具有相当普遍性的不相关性（具有Burgess型的省电性）和相应的扭曲Hecke轨道的等分布性质。这是通过利用有限域上的放大方法和黎曼假设来实现的，特别是依靠由Deligne引入并由Katz和Laumon研究的r -adic傅里叶变换。
We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on theℓ-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.