Abstract
In this work, we construct fundamental domains for congruence subgroups of SL 2 ( F q [ t ] ) and PGL 2 ( F q [ t ] ) . Our method uses Gekeler's description of the fundamental domains on the Bruhat–Tits tree X = X q + 1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma.
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