On Fourier coefficients of Maass wave forms of half integral weight belonging to Kohnen's spaces
On Fourier coefficients of Maass wave forms of half integral weight belonging to Kohnen's spaces
复制标题
属于Kohnen空间的半积分权Maass波形的傅立叶系数
DOI：
10.21099/tkbjm/1496163876
复制
发表时间：
1999
影响因子：
0.7
通讯作者：
H. Kojima
中科院分区：
文献类型：
--
作者：
H. Kojima
Waldspurger[15]证明了如果$f(Z)对应于$F$，且$f$对应于$F$，则半整权模形式$f(Z)=\sum_{n=1}^a(N)e[NZ]$在自由平方整数$n$处的傅立叶系数$a(N)$的平方本质上正比于依附于偶整重模形式$F$的Zeta函数的临界值。Kohnen-Zagier[2]，[4]明确地确定了属于Kohnen空间的模形式的比例常数
Waldspurger [15] proved that the squares of Fourier coefficients $a(n)$ at a square free integer $n$ of a modular form $f(z)=\sum_{n=1}^{\infty}a(n)e[nz]$ of half integral weight are essentially proportional to the critical value of the zeta function at a certain integer attached to the modular form $F$ of even integral weight if $f$ corresponds to $F$ by the Shimura correspondence $\Psi$ and $f$ is an eigen-function of Hecke operators. Kohnen-Zagier [2], [4] determined explicitly the constant of the proportionality in the case of modular forms of belonging to Kohnen’s spaces