On Drinfeld modular forms of higher rank III: The analogue of the k/12-formula
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DOI: 10.1016/j.jnt.2018.04.018
Abstract: Continuing the work of \cite{7} and \cite{8}, we derive an analogue of the classical "$k/12$-formula" for Drinfeld modular forms of rank $r \geq 2$. Here the vanishing order $\nu_{\omega}(f)$ of one modular form at some… read more here.
Keywords: forms higher; analogue; drinfeld modular; modular forms ... See more keywords
A basis for the space of weakly holomorphic Drinfeld modular forms for GL2(A)
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DOI: 10.1016/j.jnt.2019.03.020
Abstract: Abstract We construct a canonical basis for the space of weakly holomorphic Drinfeld modular forms. And we find that the basis elements satisfy a generating function and the duality among coefficients of the basis elements.… read more here.
Keywords: weakly holomorphic; holomorphic drinfeld; basis; basis space ... See more keywords
Satake compactification of analytic Drinfeld modular varieties
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DOI: 10.1016/j.jnt.2020.09.018
Abstract: Abstract We construct a normal projective rigid analytic compactification of an arbitrary Drinfeld modular variety whose boundary is stratified by modular varieties of smaller dimensions. This generalizes work of Kapranov. Using an algebraic modular compactification… read more here.
Keywords: drinfeld modular; compactification; analytic drinfeld; analytic compactification ... See more keywords
On Drinfeld modular curves for SL(2)
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DOI: 10.1142/s0129167x25500442
Abstract: We study the Drinfeld modular curves arising from the Hecke congruence subgroups of $\mathrm{SL}_2(\mathbb{F}_q[T])$. Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the genus… read more here.
Keywords: modular curves; drinfeld modular;