Sifted character sums and free quotients of Bianchi groups

Abstract

We show that the Bianchi group ${\mathrm{PSL}}_2({\mathcal{O}}_d)$, where ${\mathcal{O}}_d$ is the ring of integers in $\Q(\sqrt{d})$, $d<0$, has a free quotient of rank $\ge |d{|}^{1/4-\epsilon }$, as $|d|\to \infty$.

References in corpus (1)

• Primes in short arithmetic progressions