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arXiv · 0909.0799

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

A. W. Mason·Andreas Schweizer
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Abstract

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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A. W. Mason, Andreas Schweizer. 2011-07-08. The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain. https://doi.org/10.1112/plms%2Fpdr071

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