Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Dutta, Parikshit, Ghoshal, Debashis
Institutions: Asutosh College, Jawaharlal Nehru University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3007730792