Counting Cusps of Subgroups of Psl2(ok)
نویسندگان
چکیده
Let K be a number field with r real places and s complex places, and let OK be the ring of integers of K. The quotient [H]×[H]/PSL2(OK) has hK cusps, where hK is the class number of K. We show that under the assumption of the generalized Riemann hypothesis that if K is not Q or an imaginary quadratic field and if i ∈ K, then PSL2(OK) has infinitely many maximal subgroups with hK cusps. A key element in the proof is a connection to Artin’s Primitive Root Conjecture.
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