Twisted Poincaré series and zeta functions on finite quotients of buildings

Ming-Hsuan Kang*, Rupert McCallum

*Corresponding author for this work

研究成果: Article同行評審

摘要

In the case where G= SL 2 (F) for a non-archimedean local field F and Γ is a discrete torsion-free cocompact subgroup of G, there is a known relationship between the Ihara zeta function for the quotient of the Bruhat–Tits tree of G by the action of Γ, and an alternating product of determinants of twisted Poincaré series for parabolic subgroups of the affine Weyl group of G. We show how this can be generalized to other split simple algebraic groups of rank two over F and formulate a conjecture about how this might be generalized to groups of higher rank.

原文English
頁(從 - 到)309-336
頁數28
期刊Journal of Algebraic Combinatorics
49
發行號3
DOIs
出版狀態Published - 15 五月 2019

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