Pseudodifferential Operators on ${\mathbf{Q}}_p$ and $L$-Series

Parikshit Dutta, Debashis Ghoshal

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…