A $p$-arton Model for Modular Cusp Forms
| Autor: | Dutta, Parikshit, Ghoshal, Debashis |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0040577921100068 |
| Popis: | We propose to associate to a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequence in terms of the Mellin transforms and the $L$-functions related to the forms. Further we discuss the case of products of Dirichlet $L$-functions and their Mellin duals, which are convolution products of $\vartheta$-series. The latter are intriguingly similar to non-holomorphic Maass forms of weight zero as suggested by their Fourier coefficients. Comment: 1+23 pages, 1 appendix, v2: typos corrected, references added |
| Databáze: | arXiv |
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