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Journal of the London Mathematical Society Advance Access originally published online on November 22, 2007
Journal of the London Mathematical Society 2008 77(1):69-82; doi:10.1112/jlms/jdm068
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© 2007 London Mathematical Society

Zeta functions of Lie rings of upper-triangular matrices

Luke Woodward

Mathematical Institute
24–29 St Giles
Oxford OX1 3LB
United Kingdom
woodward{at}maths.ox.ac.uk
Current address:
Tessella Support Services plc
3, Vineyard Chambers
Abingdon
Oxfordshire OX14 3PX
United Kingdom

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.

2000 Mathematics Subject Classification 11M41, 17B30.

Received August 16, 2006; revised February 19, 2007; published online November 22, 2007.


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