TY - JOUR
T1 - Counting cusps of subgroups of PSL 2(OK)
AU - Petersen, Kathleen L.
PY - 2008/7
Y1 - 2008/7
N2 - Let K be a number field with r real places and s complex places, and let O K be the ring of integers of K. The quotient [ℍ 2] r x [ℍ 3] s/PSL 2(O K) has h k cusps, where h k 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 PSL 2(O k) has infinitely many maximal subgroups with h K cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.
AB - Let K be a number field with r real places and s complex places, and let O K be the ring of integers of K. The quotient [ℍ 2] r x [ℍ 3] s/PSL 2(O K) has h k cusps, where h k 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 PSL 2(O k) has infinitely many maximal subgroups with h K cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.
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U2 - 10.1090/S0002-9939-08-09262-9
DO - 10.1090/S0002-9939-08-09262-9
M3 - Article
AN - SCOPUS:77950799131
SN - 0002-9939
VL - 136
SP - 2387
EP - 2393
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -