论文标题
固定判别剂的二元二元形式表示尖端形式的傅立叶系数的平均估计和符号变化
Average estimates and sign change of Fourier coefficients of cusp forms at integers represented by binary quadratic form of fixed discriminant
论文作者
论文摘要
在本文中，我们建立了在整数支持的Hecke特征形式的归一化傅里叶系数的平均行为，该系数由任何原始的积分正定二进制二进制二进制二进制二进制二进制形式的固定判别$ d <0 $时，当时类别$ h（d）= 1 $。 我们还获得了定量结果，以符合标准化的傅立叶系数的符号变化数量$λ_{f}（n）$的hecke eigenforms $ f $，其中$ n $由任何原始的积极积极积极积极积极的确定二元定义的二进制二进制二进制二元形式的固定固定差异$ d <0 $ d $ d $ d $ d $ d $ d <0 $ $ $ x $。
In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant $D < 0$ when the class number $h(D) = 1$. We also obtain a quantitative result for the number of sign changes of the sequence of the normalised Fourier coefficients $λ_{f}(n)$ of the Hecke eigenforms $f$ where $n$ is represented by any primitive integral positive definite binary quadratic form of fixed discriminant $D < 0$ when the class number $h(D) = 1$ in the interval $(x,2x]$, for sufficiently large $x$.
