Arithmetic groups have rational representation growth

• 成果类型: Article
• 署名作者: Avni, Nir
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.2.6
• 发表日期: 2011
• 页码: 1009-1056
• 关键词: congruence subgroup problem; zeta-functions; integration; FIELDS

摘要

Let Gamma be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if Gamma has the congruence subgroup property, then the number of n-dimensional irreducible representations of Gamma grows like n(alpha), where alpha is a rational number.