The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain

Details The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain

2009-09-04

arxiv.org/abs/0909.0799v2

Mathematics

Group Theory

40 pages, refereed version, minor changes, second author's address updated

Scientific paper

We extend some algebraic properties of the classical modular group SL_2(Z) to equivalent groups in the theory of Drinfeld modules, in particular properties which are important in the theory of modular curves. We study cusp amplitudes and the level of a (congruence) subgroup of SL_2(D) for any Dedekind domain D, as ideals of D. In particular, we extend a remarkable result of Larcher. We introduce finer notions of quasi-amplitude and quasi-level, which are not required to be ideals and encode more information about the subgroup. Our results also provide several new necessary conditions for a subgroup of SL_2(D) to be a congruence subgroup.

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