论文标题
关于半整合体重模块化形式的系数和Bruinier-Kohnen猜想的分布
On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
论文作者
论文摘要
这项工作代表了一项系统的计算研究，对cuspidal hecke特征形式的傅立叶系数的分布为$γ_0（4）$和半积分权重。基于实质性计算，是否可以通过广义高斯分布来近似具有界指数的标准化傅立叶系数的分布。此外，有人认为，数据的明显对称性为符号的迹象表明了迹象的平等分配，甚至暗示了符号和绝对值是独立分布的。
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $Γ_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
