Title of article :
On the Analytic Continuation of the
Minakshisundaram]Pleijel Zeta Function for Compact
Symmetric Spaces of Rank One
Author/Authors :
Roberto Camporesi*، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 1997
Abstract :
We give two equivalent analytic continuations of the Minakshisundaram]Pleijel
zeta function zUrK z. for a Riemannian symmetric space of the compact type of
rank one UrK. First we prove that zUrK can be written as
zUrK z.seip zyNr2.VUrKzGrK z. qF z.,
where Nsdim UrK, VUrKis the volume of UrK, zGrK z. is the local zeta
function for GrK the noncompact symmetric space dual to UrK., and F z. is an
analytic function which is given explicitly as a contour integral cf. Eq. 4.11... To
prove the above formula we use a relation first noticed by Vretare.between the
scalar degeneracies of the Laplacian on UrK and the Plancherel measure on
GrK. The second expression we obtain for zUrK z. is in terms of a series of
generalized.Riemann zeta functions zR z, q. cf. Eq. 5.9... The doubly connected
case of real projective spaces is also discussed.
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications