论文标题
一类与有限字段曲线相关的功能身份
A class of functional identities associated to curves over finite fields
论文作者
论文摘要
在某些情况下，可以找到戈斯Zeta值的评估，作为对有限字段$ \ mathbb {f} _q $的新型刚性分析功能的评估，称为“ pellarin $ l $ -series”。在属$ 0 $和$ 1 $的情况下，Pellarin和Green- Papanikolas进一步确定了Pellarin $ L $ Series的功能身份，与Dirichlet $ L $ Series的功能方程相比，部分类似于。 本文的目的是证明这些功能身份的概括在任意属中存在。我们的证明利用了曲线$ x $上除法的拓扑性质，并引入了“伴随的shtuka函数”。这使我们可以重新解释Pellarin $ L $ series作为Anglès，Ngo Dac和Tavares Ribeiro研究的特殊功能的双版本。
Goss zeta values can be found, in some cases, as evaluations of a new type of rigid analytic function on projective curves $X$ over a finite field $\mathbb{F}_q$, called "Pellarin $L$-series". In the case of genus $0$ and $1$, Pellarin and Green--Papanikolas further determined functional identities for Pellarin $L$-series, in partial analogy with the functional equation of Dirichlet $L$-series. The aim of this paper is to prove that a generalization of these functional identities holds in arbitrary genus. Our proof exploits the topological nature of divisors on the curve $X$, as well as the introduction of an "adjoint shtuka function". This allows us to reinterpret Pellarin $L$-series as dual versions of the special functions studied by Anglès, Ngo Dac, and Tavares Ribeiro.
