On the structure and slopes of Drinfeld cusp forms
| Autor: | Bandini, Andrea, Valentino, Maria |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/10586458.2019.1671921 |
| Popis: | We define oldforms and newforms for Drinfeld cusp forms of level $t$ and conjecture that their direct sum is the whole space of cusp forms. Moreover we describe explicitly the matrix $U$ associated to the action of the Atkin operator $\mathbf{U}_t$ on cusp forms of level $t$ and use it to compute tables of slopes of eigenforms. Building on such data, we formulate conjectures on bounds for slopes, on the diagonalizability of $\mathbf{U}_t$ and on various other issues. Via the explicit form of the matrix $U$ we are then able to verify our conjectures in various cases (mainly in small weights). Comment: Final version, to appear in Exp. Math |
| Databáze: | arXiv |
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