Pseudodifferential Operators on $\mathbf{Q}_p$ and $L$-Series
| Autor: | Dutta, Parikshit, Ghoshal, Debashis |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 1+13 pages, 1 figure |
| Databáze: | arXiv |
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