Counting cusps of subgroups of  <IMG WIDTH="99" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="/proc/2008-136-07/S0002-9939-08-09262-9/gif-title0/img1.gif" ALT="$ mathrm{PSL}_2(mathcal{O}_K)$">期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Counting cusps of subgroups of $mathrm{PSL}_2(mathcal{O}_K)$

Authors:	Kathleen L. Petersen

Affiliation:	Department of Mathematics and Statistics, Queen's University, Kingston, Ontario K7L 3N6, Canada

Abstract:	Let be a number field with real places and complex places, and let $mathcal{O}_K$ be the ring of integers of . The quotient $[mathbb{H}^2]^rtimes [mathbb{H}^3]^s/mathrm{PSL}_2(mathcal{O}_K)$ has cusps, where is the class number of . We show that under the assumption of the generalized Riemann hypothesis that if is not or an imaginary quadratic field and if , then $mathrm{PSL}_2(mathcal{O}_K)$ has infinitely many maximal subgroups with cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文