Abstract
An explicit formula is given for the number of subgroups of indexp n in the principle congruence subgroups of SL2(ℤ p ) (for odd primesp), and for the zeta function associated with the group. Asymptotically this number iscnp n , wherec is a constant depending on the congruence subgroup. Also, the zeta function of thei-th congruence subgroup coincides with the partial zeta function of the 3-generated subgroups of thei+1-th congruence subgroup, and for each indexp n the ratio between 2-generated subgroups and 3-generated subgroups tends top - 1:1, asn tends to infinity.
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