▁of ▁its ▁Lie ▁algebra , ▁together ▁with ▁the ▁W ey l ▁dimension ▁formula , ▁implies ▁that ▁ ▁can ▁be ▁written ▁as ▁ ▁where ▁ ▁denotes ▁the ▁set ▁of ▁positive ▁roots , ▁ ▁is ▁a ▁set ▁of ▁simple ▁roots ▁and ▁ ▁is ▁the ▁rank . ▁ ▁Ex amples ▁▁▁ ▁, ▁the ▁Riemann ▁z eta ▁function . ▁ ▁Ab sc issa ▁of ▁convergence ▁ ▁If ▁ ▁is ▁simple ▁and ▁simply ▁connected , ▁the ▁ab sc issa ▁of ▁convergence ▁of ▁ ▁is ▁, ▁where ▁ ▁is ▁the ▁rank ▁and ▁. ▁This ▁is ▁a ▁theorem ▁due ▁to ▁Alex ▁Lub ot z ky ▁and ▁Michael ▁Lars en . ▁A ▁new ▁proof ▁is ▁given ▁by ▁J ok ke ▁H äs ä ▁and ▁Alexander ▁St as in ski ▁in . ▁The ▁proof ▁in ▁ ▁yields ▁a ▁more ▁general ▁result , ▁namely ▁it ▁gives ▁an ▁explicit ▁value ▁( in ▁terms ▁of ▁simple ▁combin ator ics ) ▁of ▁the ▁ab sc issa ▁of ▁convergence ▁of ▁any ▁" M ell in ▁z eta ▁function " ▁of ▁the ▁form ▁ ▁where ▁ ▁is ▁a ▁product ▁of ▁linear ▁polynomials ▁with ▁non - negative ▁real ▁coefficients . ▁ ▁References ▁ ▁Category : Z eta ▁and ▁L - functions <0x0A> </s> ▁Parker ' s ▁Not ch , ▁named ▁after ▁former ▁Commission er ▁of ▁the ▁North west ▁Territ ories , ▁John ▁H avel ock ▁Parker , ▁is ▁a ▁pro tr usion ▁of ▁the ▁North west ▁Territ ories ▁south wards ▁into ▁N un av ut ▁on ▁Victoria ▁Island . ▁In ▁the ▁North west ▁Territ ories ▁the ▁pro tr usion