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Sifted character sums and free quotients of Bianchi groups

Published online by Cambridge University Press:  28 September 2006

JAN–CHRISTOPH SCHLAGE–PUCHTA
JAN–CHRISTOPH SCHLAGE–PUCHTA
Affiliation:
Mathematisches Institut, Eckerstr. 1, 79104 Freiburg, Germany. e-mail: jcp@arcade.mathematik.uni-freiburg.de
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Abstract

We show that the Bianchi group $\mathrm{PSL}_2(\mathcal{O}_d)$, where $\mathcal{O}_d$ is the ring of integers in $\mathbb{Q}(\sqrt{d})$, $d\,{<}\,0$, has a free quotient of rank$\,{\geq}\, |d|^{\frac {1}{4}-\epsilon}$, as $|d|\,{\to}\,\infty$. To do so, we give an estimate for a sifted character sum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 2 , September 2006 , pp. 205 - 207
Copyright
2006 Cambridge Philosophical Society

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