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

28 Feb 2020 Dutta Parikshit Ghoshal Debashis

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 $L^2(\mathbf{Q}_p)$... (read more)

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# Categories

• NUMBER THEORY
• HIGH ENERGY PHYSICS - THEORY