Year: 2019
Type: article
Abstract: 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 Ut 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 Ut 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).
Source: Experimental Mathematics
Authors: Andrea Bandini, Maria Valentino
Institutions: University of Pisa, University of Parma
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2903188712