Local Functional Equations for Submodule Zeta Functions Associated to Nilpotent Algebras of Endomorphisms
Voll, Christopher
Voll
Christopher
We give a sufficient criterion for generic local functional equations for submodule zeta functions associated to nilpotent algebras of endomorphisms defined over number fields. This allows us, in particular, to prove various conjectures on such functional equations for ideal zeta functions of nilpotent Lie lattices. Via the Mal'cev correspondence, these results have corollaries pertaining to zeta functions enumerating normal subgroups of finite index in finitely generated nilpotent groups, most notably finitely generated free nilpotent groups of any given class.
2019
7
2137-2176
2137-2176
Oxford Univ Press
2019