论文标题
算术进展和全态投影中Hurwitz班级数量的矩分布
Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection
论文作者
论文摘要
在本文中，我们研究了与固定算术渐进性相关的hurwitz类数量的时刻。特别是，我们将$ t $固定在算术进程中$ t \ equiv m \ pmod {m} $，并考虑$ h（4n-t^2）$的$ 2k $ - $ 3矩与零矩的比率，因为一种变化$ n $。因此，特殊情况$ n = p^r $从椭圆曲线上的椭圆曲线上的有限曲线上的有限磁场上的$ p^r $元素上的eLliptic曲线上的trace $ t \ equiv m \ pmod {m} $产生渐近公式。
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix $t$ in an arithmetic progression $t\equiv m\pmod{M}$ and consider the ratio of the $2k$-th moment to the zeroeth moment for $H(4n-t^2)$ as one varies $n$. The special case $n=p^r$ yields as a consequence asymptotic formulas for moments of the trace $t\equiv m\pmod{M}$ of Frobenius on elliptic curves over finite fields with $p^r$ elements.
