论文标题
$ \ Mathbf {q} _p $和$ l $ -Series上的pseudoDifferential运算符
Pseudodifferential Operators on $\mathbf{Q}_p$ and $L$-Series
论文作者
论文摘要
我们在Hilbert Space $ l^2（\ Mathbf {q} _p）$上定义了一个伪差操作员的家族。 Riemann zeta功能和相关的dirichlet $ l $ functions可以在$ l^2（\ mathbf {q} _p）$的子空间上表示为这些操作员的跟踪。我们还将其扩展到与模块化（CUSP）表单相关的$ L $ functions。 $ l^2（\ mathbf {q} _p）$上的小波是这些运算符的特征函数的常见集。
We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann zeta-function and the related Dirichlet $L$-functions can be expressed as a trace of these operators on a subspace of $L^2(\mathbf{Q}_p)$. We also extend this to the $L$-functions associated with modular (cusp) forms. Wavelets on $L^2(\mathbf{Q}_p)$ are common sets of eigenfunctions of these operators.
