论文标题
Hecke组的Raleigh-Akiyama多项式的有限野外模型
Finite field models of Raleigh-Akiyama polynomials for Hecke groups
论文作者
论文摘要
继罗利和阿基山的工作之后 （\ cite {raleigh1962fourier，akiyama1992note}），在\ cite {Interpolating}中，我们考虑了（除其他对象）重量零meromorthic模块化表单$ j_m $ j_m $的家族，用于Hecke $ g（λ_m）$。我们在\ cite {Interpolation}中猜想，对于某些均匀化$ x_m $，$ j_m $具有傅立叶扩展$ j_m = 1/x_m + \ sum_ {n = 0}^{\ infty} a_n（m） $ \ mathbb {q} [x] $。本文与$ a_n（x）$的模型$ \ Mathcal {a} _n [p]（x）$：代表具有特征性$ p $的有限字段的自图。主要内容是基于数值实验的某些家族的$ \ Mathcal {a} _n [p]（x）$的猜想。
Following work of Raleigh and Akiyama (\cite{raleigh1962fourier, akiyama1992note}), in \cite{interpolating} we considered (among other objects) families of weight zero meromorphic modular forms $J_m$ for Hecke groups $G(λ_m)$. We conjectured in \cite{interpolating} that, for a certain uniformizing variable $X_m$, the $J_m$ have Fourier expansions $J_m = 1/X_m + \sum_{n = 0}^{\infty} A_n(m) X_m^n$, where the $A_n(x)$ are polynomials in $\mathbb{Q}[x]$. The present article is concerned with models $\mathcal{A}_n[p](x)$ of the $A_n(x)$: polynomials representing self-maps of finite fields with characteristic $p$. The main content is a conjecture specifying $\mathcal{A}_n[p](x)$ up to a multiplicative constant for certain families of $n$ and $p$, based on numerical experiments.
