Ellam, DC; (2013) An approach to the congruence subgroup problem via fractional weight modular forms. Doctoral thesis , UCL (University College London).

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Abstract

In this thesis we develop a new criterion for the congruence subgroup problem in the case of arithmetic groups of $\SU(2,1)$, which in principle can be checked using a computer. Our main theorem states that if there exists a prime $q>3$ and a congruence subgroup $\Gamma'\subset \SU(2,1)(\Z)$ such that the restriction map $H^{2}(\SU(2,1)(\Z), \F_{q}) \rightarrow H^{2}(\Gamma',\F_{q})$ is not injective, then the congruence kernel of $\SU(2,1)$ is infinite.

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