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Zeta functions of Lie rings of upper‐triangular matrices
Author(s) -
Woodward Luke
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm068
Subject(s) - mathematics , quotient , pure mathematics , ideal (ethics) , riemann zeta function , lie group , functional equation , arithmetic zeta function , algebra over a field , mathematical analysis , partial differential equation , philosophy , epistemology
We prove a two‐part theorem on local ideal zeta functions of Lie rings of upper‐triangular matrices. First, we prove that these local zeta functions display a strong uniformity. Secondly, we prove that these zeta functions satisfy a local functional equation. Some explicit examples of these zeta functions are also presented. Finally, we consider certain quotients of these Lie rings, showing that the strong uniformity continues to hold, and that under certain circumstances the functional equation does too.